Aufgaben:Exercise 3.6Z: Examination Correction - Revision history

Guenter at 15:05, 17 February 2022

2022-02-17T15:05:35Z

Bene: Text replacement - "rms value" to "standard deviation"

2022-02-17T11:11:39Z

Text replacement - "rms value" to "standard deviation"

Bene: Text replacement - "root mean square" to "standard deviation"

2022-02-17T11:00:51Z

Text replacement - "root mean square" to "standard deviation"

Guenter at 15:03, 1 February 2022

2022-02-01T15:03:33Z

Guenter at 14:50, 1 February 2022

2022-02-01T14:50:26Z

Noah at 23:40, 1 January 2022

2022-01-01T23:40:59Z

Noah at 19:41, 1 January 2022

2022-01-01T19:41:02Z

Guenter at 10:18, 20 December 2021

2021-12-20T10:18:25Z

Guenter: Guenter moved page Aufgaben:Aufgabe 3.6Z: Prüfungskorrektur to Aufgaben:Exercise 3.6Z: Examination Correction

2021-12-20T10:14:42Z

Guenter moved page Aufgabe 3.6Z: Prüfungskorrektur to Exercise 3.6Z: Examination Correction

Javier: Text replacement - "”" to """

2021-05-28T14:31:48Z

Text replacement - "”" to """

@@ Line 8: / Line 8: @@
 Further,&nbsp; the exercise must take into account:
 *The maximum achievable score is&nbsp; $100$.&nbsp; The best student achieved&nbsp; $88$&nbsp; points.
-*Due to the relatively large number of participants,&nbsp; the achieved score &ndash; this is the random variable&nbsp; $z$&nbsp; &ndash; has with good approximation a&nbsp; [[Theory_of_Stochastic_Signals/Gaussian_Distributed_Random_Variables#Probability_density_function_.26_cumulative_density_function|Gaussian distribution]]&nbsp; with mean&nbsp; $m_z = 60$&nbsp; and standard deviation&nbsp; (standard deviation)&nbsp; $\sigma_z = 10$.
+*Due to the relatively large number of participants,&nbsp; the achieved score &ndash; this is the random variable&nbsp; $z$&nbsp; &ndash; has with good approximation a&nbsp; [[Theory_of_Stochastic_Signals/Gaussian_Distributed_Random_Variables#Probability_density_function_.26_cumulative_density_function|Gaussian distribution]]&nbsp; with mean&nbsp; $m_z = 60$&nbsp; and standard deviation&nbsp;  $\sigma_z = 10$.
-*In the correction,&nbsp; not only whole scores were assigned,&nbsp; but also&nbsp; (arbitrary)&nbsp; intermediate&nbsp; values, so that the random variable&nbsp; $z$&nbsp; can be taken as&nbsp; "continuous valued"&nbsp; with good approximation.
+*In the correction,&nbs

@@ Line 25: / Line 25: @@
 *The exercise belongs to the chapter&nbsp; [[Theory_of_Stochastic_Signals/Gaussian_Distributed_Random_Variables|Gaussian distributed random variables]].
 *The&nbsp; "Gaussian distribution"&nbsp; is often called&nbsp; "normal distribution".&nbsp; This is not quite correct:
-*A normally distributed random variable&nbsp; $z$&nbsp; does have a Gaussian PDF and CDF,&nbsp; but always with mean&nbsp; $m_z = 0$&nbsp; and rms value&nbsp; $\sigma_z = 1$.
+*A normally distributed random variable&nbsp; $z$&nbsp; does have a Gaussian PDF and CDF,&nbsp; but always with mean&nbsp; $m_z = 0$&nbsp; and standard deviation&nbsp; $\sigma_z = 1$.
@@ Line 77: / Line 77: @@
 '''(2)'''&nbsp; One gets a&nbsp; "1.0"&nbsp; with&nbsp; $82$&nbsp; points or more.&nbsp;
-*Therefore,&nbsp; with the mean&nbsp; $m_z = 60$&nbsp; and the rms value&nbsp; $\sigma_z = 10$:
+*Therefore,&nbsp; with the mean&nbsp; $m_z = 60$&nbsp; and the standard deviation&nbsp; $\sigma_z = 10$:
 :$$\rm Pr(\it z\ge \rm 82)=\rm Q\Bigg(\frac{\rm 82-60}{\rm 10}\Bigg)=\rm Q(\rm 2.2)
 \hspace{0.15cm}{=\rm 0.0139}.$$

@@ Line 8: / Line 8: @@
 Further,&nbsp; the exercise must take into account:
 *The maximum achievable score is&nbsp; $100$.&nbsp; The best student achieved&nbsp; $88$&nbsp; points.
-*Due to the relatively large number of participants,&nbsp; the achieved score &ndash; this is the random variable&nbsp; $z$&nbsp; &ndash; has with good approximation a&nbsp; [[Theory_of_Stochastic_Signals/Gaussian_Distributed_Random_Variables#Probability_density_function_.26_cumulative_density_function|Gaussian distribution]]&nbsp; with mean&nbsp; $m_z = 60$&nbsp; and root mean square&nbsp; (standard deviation)&nbsp; $\sigma_z = 10$.
+*Due to the relatively large number of participants,&nbsp; the achieved score &ndash; this is the random variable&nbsp; $z$&nbsp; &ndash; has with good approximation a&nbsp; [[Theory_of_Stochastic_Signals/Gaussian_Distributed_Random_Variables#Probability_density_function_.26_cumulative_density_function|Gaussian distribution]]&nbsp; with mean&nbsp; $m_z = 60$&nbsp; and standard deviation&nbsp; (standard deviation)&nbsp; $\sigma_z = 10$.
 *In the correction,&nbsp; not only whole scores were assigned,&nbsp; but also&nbsp; (arbitrary)&nbsp; intermediate&nbsp; values, so that the random variable&nbsp; $z$&nbsp; can be taken as&nbsp; "continuous valued"&nbsp; with good approximation.

@@ Line 67: / Line 67: @@
 ===Solution===
 {{ML-Kopf}}
-'''(1)'''&nbsp; Correct are <u>the solutions 1 and 3</u>:
+'''(1)'''&nbsp; Correct are&nbsp; <u>the solutions 1 and 3</u>:
-*According to the central limit theorem, a Gaussian distribution is obtained for the sum of many independent quantities.
+*According to the central limit theorem,&nbsp; a Gaussian distribution is obtained for the sum of many independent quantities.
-*Conversely, if there are only a few dependent tasks, there is no Gaussian distribution.
+*Conversely,&nbsp; if there are only a few dependent tasks,&nbsp; there is no Gaussian distribution.
-*A single yes/no question leads to a two-point distribution ($0$ points or maximum number of points).
+*A single yes/no question leads to a two-point distribution&nbsp; ($0$ points or maximum number of points).
-*Even if these imperatives are followed, a Gaussian distribution will not be expected for very few participants.
+*Even if these imperatives are followed,&nbsp; a Gaussian distribution will not be expected for very few participants.
-'''(2)'''&nbsp; One gets a "1.0" with&nbsp; $82$&nbsp; points or more.&nbsp;
+'''(2)'''&nbsp; One gets a&nbsp; "1.0"&nbsp; with&nbsp; $82$&nbsp; points or more.&nbsp;
-*Therefore, with the mean&nbsp; $m_z = 60$&nbsp; and the rms&nbsp; $\sigma_z = 10$:
+*Therefore,&nbsp; with the mean&nbsp; $m_z = 60$&nbsp; and the rms value&nbsp; $\sigma_z = 10$:
 :$$\rm Pr(\it z\ge \rm 82)=\rm Q\Bigg(\frac{\rm 82-60}{\rm 10}\Bigg)=\rm Q(\rm 2.2)
 \hspace{0.15cm}{=\rm 0.0139}.$$
-*For a thousand participants, it follows&nbsp; $N_\text{1.0}\hspace{0.15cm}\underline{= 14}$.
+*For a thousand participants,&nbsp; it follows&nbsp; $N_\text{1.0}\hspace{0.15cm}\underline{= 14}$.
@@ Line 86: / Line 86: @@
 '''(3)'''&nbsp; With less than&nbsp; $46$&nbsp; points, one has failed the exam:
 :$$\rm Pr(\it z<\rm 46)=\rm Pr(\it z \le \rm 46)=\rm \phi\Bigg(\frac{\rm 46-60}{\rm 10}\Bigg)=\rm \phi(\rm -1.4)=\rm Q(\rm 1.4)=\rm 0.0807.$$
-*So <u>81 students have to compete again</u>.
+*So&nbsp; <u>81 students have to compete again</u>.
-'''(4)'''&nbsp; The difference in points&nbsp; $82 - 46 = 36$&nbsp; must be divided among nine grade intervals&nbsp; $(1.3$, ... , $4.0)$&nbsp; .
+'''(4)'''&nbsp; The difference in points&nbsp; $82 - 46 = 36$&nbsp; must be divided among nine grade intervals&nbsp; $(1.3$, ... , $4.0)$.
 *Each interval thus comprises&nbsp; $4$&nbsp; points.
-*For example, one receives a grade of "3.0" if one&nbsp; $58$&nbsp; to&nbsp; $62$&nbsp; points.
+*For example,&nbsp; one receives a grade of&nbsp; "3.0"&nbsp; if one has&nbsp; $58$&nbsp; to&nbsp; $62$&nbsp; points.
-*The probability that the grade is in this range is given by.
+*The probability that the grade is in this range is given by
 :$$\rm Pr(\rm 58 <\it z<\rm 62)=\rm \phi\Bigg(\frac{\rm 62-60}{\rm 10}\Bigg)-\rm \phi\Bigg(\frac{\rm 58-60}{\rm 10}\Bigg).$$
-Taking advantage of the symmetry, one obtains:
+*Taking advantage of the symmetry,&nbsp; one obtains:
 :$$\rm Pr(\rm 58 <\it z<\rm 62) = \rm \phi(\rm 0.2)-\rm \phi(\rm -0.2) = \rm 0.5792-\rm 0.4207=0.1587\hspace{0.2cm}\hspace{0.15cm}\underline{(159 \hspace{0.1cm}\rm participants)}.$$
-''Notes:''
+Notes:
-*$z$&nbsp; is to be taken as a continuous random variable. Therefore, the score&nbsp; $62$&nbsp; is simultaneously the upper bound for the "3.0"&ndash;range as well as the lower bound for the grade "2.7."
+*$z$&nbsp; is to be taken as a continuous valued random variable.&nbsp;
-*If&nbsp; $z$&nbsp; were only an integer, then&nbsp; $62$&nbsp; would have to be assigned to either the "2.7" grade or the "3.0" grade, depending on the mood of the corrector.&nbsp; Of course, this would have to be done in the same way for all examinees.
+*Therefore,&nbsp; the score&nbsp; $62$&nbsp; is simultaneously the upper bound for the grade&nbsp; "3.0"&nbsp; as well as the lower bound for the grade&nbsp; "2.7."
-'''(5)'''&nbsp; Analogous to the sample solution of the subtask&nbsp; '''(4)'''&nbsp; applies to the grade "2.7":
+'''(5)'''&nbsp; Analogous to the solution of the subtask&nbsp; '''(4)'''&nbsp; applies to the grade&nbsp; "2.7":
 :$$\rm Pr(\rm 62 <\it z<\rm 66)=\rm \phi(\rm 0.6)-\rm \phi(\rm 0.2)=\rm 0.7257-\rm 0.5792=0.1465.$$
-*For reasons of symmetry, the same value is obtained for the grade "3.3":
+*For reasons of symmetry,&nbsp; the same value is obtained for the grade&nbsp; "3.3":
 :$$\rm Pr(\rm 54 <\it z<\rm 58)=\rm \phi(-\rm 0.2)-\rm \phi(-\rm 0.6)= \rm Q(\rm 0.2)-\rm Q(\rm 0.6)=\rm 0.1465.$$
-*So <u>each 146 participants receive a grade of "2.7" or "3.3"</u>.
+*So&nbsp; <u>each 146 participants receive a grade of&nbsp; "2.7"&nbsp; or&nbsp; "3.3"</u>.
-'''(6)'''&nbsp; With the points&ndash;scores&ndash;assignment made here, not only are the points distributed around&nbsp; $m_z = 60$&nbsp; symmetrically, but also the scores around&nbsp; "3.0".&nbsp; There are
+'''(6)'''&nbsp; With the points/grade assignment made here,&nbsp; not only the points are distributed around&nbsp; $m_z = 60$&nbsp; symmetrically,&nbsp; but also the scores around&nbsp; "3.0".&nbsp; There are
-*exactly as many "2.7"s as "3.3"s&nbsp; $($around&nbsp; $±0.3$&nbsp; away from&nbsp; $3.0$&nbsp;$)$,
+*exactly as many&nbsp; "2.7"s&nbsp; as&nbsp; "3.3"s&nbsp; $($around&nbsp; $±0.3$&nbsp; away from&nbsp; $3.0$&nbsp;$)$,
-*exactly as many "2.3 "s as "3.7"s&nbsp; $(3.0 ±0.7)$, and
+*exactly as many&nbsp; "2.3 "s&nbsp; as&nbsp; "3.7"s&nbsp; $(3.0 ±0.7)$, and
-*exactly as many "1.0 "s as "5.0 "s.
+*exactly as many&nbsp; "1.0 "s&nbsp; as&nbsp; "5.0 "s.
-Therefore, the $\rm mean\hspace{0.15cm} grade\hspace{0.15cm}\underline{ 3.0}$ results.
+Therefore,&nbsp; the&nbsp; $\rm mean\hspace{0.15cm} grade\hspace{0.15cm}\underline{ 3.0}$&nbsp; results.
 {{ML-Fuß}}

@@ Line 3: / Line 3: @@
 }}
-[[File:P_ID148__Sto_Z_3_6.png|right|frame|table for &nbsp;${\rm \phi}(x)$&nbsp; and&nbsp; ${\rm Q}(x)$]]
+[[File:P_ID148__Sto_Z_3_6.png|right|frame|Table for &nbsp;${\rm \phi}(x)$&nbsp; and&nbsp; ${\rm Q}(x)$]]
-In an exam at the TU Munich&nbsp; $1000$&nbsp; students participated.&nbsp; From the grade "4.0" upwards up to "1.0" the exam is considered to be passed.&nbsp; The exam regulations provide for the following grades:
+In an exam at the TU Munich&nbsp; $1000$&nbsp; students participated.&nbsp; From the grade&nbsp; "4.0"&nbsp; upwards up to&nbsp; "1.0"&nbsp; the exam is considered to be passed.&nbsp; The exam regulations provide for the following grades:
 :$$1.0, \ 1.3, \ 1.7, \ 2.0, \ 2.3, \ 2.7, \ 3.0, \ 3.3, \ 3.7, \ 4.0, \ 4.3, \ 4.7, \ 5.0.$$
-Further, the exercise must take into account:
+Further,&nbsp; the exercise must take into account:
 *The maximum achievable score is&nbsp; $100$.&nbsp; The best student achieved&nbsp; $88$&nbsp; points.
-*Due to the relatively large number of participants, the achieved score &ndash; this is the random variable&nbsp; $z$&nbsp; &ndash; with good approximation a&nbsp; [[Theory_of_Stochastic_Signals/Gaussian_Distributed_Random_Variables#Probability_density_function_.26_cumulative_density_function|Gaussian distribution]]&nbsp; with mean&nbsp; $m_z = 60$&nbsp; and rms (standard deviation)&nbsp; $\sigma_z = 10$.
+*Due to the relatively large number of participants,&nbsp; the achieved score &ndash; this is the random variable&nbsp; $z$&nbsp; &ndash; has with good approximation a&nbsp; [[Theory_of_Stochastic_Signals/Gaussian_Distributed_Random_Variables#Probability_density_function_.26_cumulative_density_function|Gaussian distribution]]&nbsp; with mean&nbsp; $m_z = 60$&nbsp; and root mean square&nbsp; (standard deviation)&nbsp; $\sigma_z = 10$.
-*In the correction, not only whole scores were assigned, but also (arbitrary) intermediate values, so that the random variable&nbsp; $z$&nbsp; can be taken as "continuous" with good approximation.
+*In the correction,&nbsp; not only whole scores were assigned,&nbsp; but also&nbsp; (arbitrary)&nbsp; intermediate&nbsp; values, so that the random variable&nbsp; $z$&nbsp; can be taken as&nbsp; "continuous valued"&nbsp; with good approximation.
-For scoring, the guidelines given are:
+For scoring,&nbsp; the guidelines given are:
-*Even with six points less than the best&nbsp; $($so from&nbsp; $82$&nbsp; points$)$&nbsp; one shall get "1.0".
+*Even with six points less than the best&nbsp; $($so from&nbsp; $82$&nbsp; points$)$&nbsp; one shall get&nbsp; "1.0".
-*If one&nbsp; $46\%$&nbsp; of the total score, one has passed the exam.
+*If one reaches&nbsp; $46\%$&nbsp; of the total score,&nbsp; one has passed the exam.
 *The points/grades assignment shall be linear.
@@ Line 23: / Line 23: @@
 Hints:
 *The exercise belongs to the chapter&nbsp; [[Theory_of_Stochastic_Signals/Gaussian_Distributed_Random_Variables|Gaussian distributed random variables]].
+*The&nbsp; "Gaussian distribution"&nbsp; is often called&nbsp; "normal distribution".&nbsp; This is not quite correct:
-*Especially in the school curriculum, the&nbsp; "Gaussian distribution"&nbsp; is often called&nbsp; "normal distribution"&nbsp; This is not quite correct:
+*A normally distributed random variable&nbsp; $z$&nbsp; does have a Gaussian PDF and CDF,&nbsp; but always with mean&nbsp; $m_z = 0$&nbsp; and rms value&nbsp; $\sigma_z = 1$.
@@ Line 32: / Line 31: @@
 <quiz display=simple>
-{What criteria should be considered in problem creation so that the grades will result in "approximately a normal distribution"?
+{What criteria should be considered in problem creation so that the grades will result in&nbsp; "approximately a normal distribution"?
 |type="[]"}
 + There are many exam participants.
@@ Line 40: / Line 39: @@
-{How many examinees are expected to score "1.0"?
+{How many examinees are expected to score&nbsp; "1.0"?
 |type="{}"}
 $N_\text{1.0} \ = \ $ { 14 3% }
-{How many examinees are likely to fail the exam?&nbsp; Take into account that&nbsp; $z$&nbsp; can be taken as a continuous random variable.
+{How many examinees are likely to fail the exam?&nbsp; Take into account that&nbsp; $z$&nbsp; can be taken as a continuous valued  random variable.
 |type="{}"}
 $N_\text{4.3 ... 5.0}  \ = \ $ { 81 3% }
-{Specify the points/grades&ndash;assignment.&nbsp; At what point do you get a "3.0"?&nbsp; How many examinees will get this grade?
+{Specify the points/grades assignment.&nbsp; At what point do you get a&nbsp; "3.0"?&nbsp; How many examinees will get this grade?
 |type="{}"}
 $N_\text{3.0} \ = \ $ { 159 3% }
-{How many examinees are expected to receive the grade "2.7"?&nbsp; Justify why exactly that many examinees will receive the grade "3.3".
+{How many examinees are expected to receive the grade "2.7"?&nbsp; Justify why exactly that many examinees will receive the grade&nbsp; "3.3".
 |type="{}"}
 $N_\text{2.7}  \ = \ $ { 146 3% }

@@ Line 1: / Line 1: @@
-{{quiz-Header|Buchseite=Stochastische Signaltheorie/Gaußverteilte Zufallsgröße
+{{quiz-Header|Buchseite=Theory_of_Stochastic_Signals/Gaussian_Distributed_Random_Variables
 }}
-[[File:P_ID148__Sto_Z_3_6.png|right|frame|Tabelle für &nbsp;${\rm \phi}(x)$&nbsp; und&nbsp; ${\rm Q}(x)$]]
+[[File:P_ID148__Sto_Z_3_6.png|right|frame|table for &nbsp;${\rm \phi}(x)$&nbsp; and&nbsp; ${\rm Q}(x)$]]
-An einer Pr&uuml;fung an der TU M&uuml;nchen haben&nbsp; $1000$&nbsp; Studentinnen und Studenten teilgenommen.&nbsp; Ab der Note "4.0" gilt die Pr&uuml;fung als bestanden.&nbsp; Die Pr&uuml;fungsordnung sieht folgende Noten vor:
+In an exam at the TU Munich&nbsp; $1000$&nbsp; students participated.&nbsp; From the grade "4.0" upwards up to "1.0" the exam is considered to be passed.&nbsp; The exam regulations provide for the following grades:
 :$$1.0, \ 1.3, \ 1.7, \ 2.0, \ 2.3, \ 2.7, \ 3.0, \ 3.3, \ 3.7, \ 4.0, \ 4.3, \ 4.7, \ 5.0.$$
-Weiter ist bei der Aufgabe zu berücksichtigen:
+Further, the exercise must take into account:
-*Die maximal erreichbare Punktzahl beträgt&nbsp; $100$.&nbsp; Der beste Student erreichte&nbsp; $88$&nbsp; Punkte.
+*The maximum achievable score is&nbsp; $100$.&nbsp; The best student achieved&nbsp; $88$&nbsp; points.
-*Aufgrund der relativ gro&szlig;en Teilnehmerzahl ergibt sich f&uuml;r die erreichte Punktzahl &ndash; dies sei die Zufallsgr&ouml;&szlig;e&nbsp; $z$&nbsp; &ndash; mit guter N&auml;herung eine&nbsp; [[Theory_of_Stochastic_Signals/Gaußverteilte_Zufallsgröße#Wahrscheinlichkeitsdichte-_und_Verteilungsfunktion|Gau&szlig;verteilung]]&nbsp; mit Mittelwert&nbsp; $m_z = 60$&nbsp; und Streuung (Standardabweichung)&nbsp; $\sigma_z = 10$.
+*Due to the relatively large number of participants, the achieved score &ndash; this is the random variable&nbsp; $z$&nbsp; &ndash; with good approximation a&nbsp; [[Theory_of_Stochastic_Signals/Gaussian_Distributed_Random_Variables#Probability_density_function_.26_cumulative_density_function|Gaussian_Distribution]]&nbsp; with mean&nbsp; $m_z = 60$&nbsp; and rms (standard deviation)&nbsp; $\sigma_z = 10$.
-*Bei der Korrektur wurden nicht nur ganze Punktzahlen vergeben, sondern auch (beliebige) Zwischenwerte, so dass man die Zufallsgröße&nbsp; $z$&nbsp; mit guter N&auml;herung als "kontinuierlich" auffassen kann.
+*In the correction, not only whole scores were assigned, but also (arbitrary) intermediate values, so that the random variable&nbsp; $z$&nbsp; can be taken as "continuous" with good approximation.
-F&uuml;r die Bewertung werden als Richtlinien vorgegeben:
+For scoring, the guidelines given are:
-*Auch mit sechs Punkten weniger als der Beste&nbsp; $($also ab&nbsp; $82$&nbsp; Punkten$)$&nbsp; soll man "1.0" bekommen.
+*Even with six points less than the best&nbsp; $($so from&nbsp; $82$&nbsp; points$)$&nbsp; one shall get "1.0".
-*Hat man&nbsp; $46\%$&nbsp; der Gesamtpunktzahl erreicht, so hat man die Pr&uuml;fung bestanden.
+*If one&nbsp; $46\%$&nbsp; of the total score, one has passed the exam.
-*Die Punkte/Noten-Zuordnung soll linear erfolgen.
+*The points/grades assignment shall be linear.
@@ Line 22: / Line 22: @@
-''Hinweise:''
+Hints:
-*Die Aufgabe gehört zum  Kapitel&nbsp; [[Theory_of_Stochastic_Signals/Gaußverteilte_Zufallsgröße|Gaußverteilte Zufallsgrößen]].
+*The exercise belongs to the chapter&nbsp; [[Theory_of_Stochastic_Signals/Gaussian_Distributed_Random_Variables|Gaussian distributed random variables]].
-*Gerade im Schulbereich wird die&nbsp; "Gaußverteilung"&nbsp;  oft als&nbsp;  "Normalverteilung"&nbsp; bezeichnet.&nbsp; Dies ist nicht ganz korrekt:
+*Especially in the school curriculum, the&nbsp; "Gaussian distribution"&nbsp; is often called&nbsp; "normal distribution"&nbsp; This is not quite correct:
-*Eine normalverteilte Zufallsgröße&nbsp; $z$&nbsp; hat zwar eine Gaußsche WDF und VTF,&nbsp; jedoch stets mit Mittelwert&nbsp; $m_z = 0$&nbsp; und Streuung&nbsp; $\sigma_z = 1$.
+*A normally distributed random variable&nbsp; $z$&nbsp; does have a Gaussian PDF and CDF,&nbsp; but always with mean&nbsp; $m_z = 0$&nbsp; and rms&nbsp; $\sigma_z = 1$.
-===Fragebogen===
+===Questions===
 <quiz display=simple>
-{Welche Kriterien sind bei der Aufgabenerstellung zu beachten, damit die Punktezahl  "etwa eine Normalverteilung" ergeben wird?
+{What criteria should be considered in problem creation so that the score will result in "approximately a normal distribution"?
 |type="[]"}
-+ Es gibt viele Pr&uuml;fungsteilnehmer.
++ There are many exam participants.
-- Die Teilaufgaben h&auml;ngen in starkem Ma&szlig;e voneinander ab.
+- The subproblems depend on each other to a large extent.
-+ Es gibt viele unabh&auml;ngige Aufgaben.
++ There are many independent problems.
-- Die Pr&uuml;fung besteht aus einer einzigen Frage mit Ja/Nein-Antwort.
+- The exam consists of a single yes/no question.
-{Wieviele Teilnehmer werden voraussichtlich mit „1.0“ abschlie&szlig;en?
+{How many examinees are expected to score "1.0"?
 |type="{}"}
 $N_\text{1.0} \ = \ $ { 14 3% }
-{Wieviele Teilnehmer werden die Prüfung  wohl nicht bestehen?&nbsp; Ber&uuml;cksichtigen Sie, dass man&nbsp; $z$&nbsp; als kontinuierliche Zufallsgr&ouml;&szlig;e auffassen kann.
+{How many examinees are likely to fail the exam?&nbsp; Take into account that&nbsp; $z$&nbsp; can be taken as a continuous random variable.
 |type="{}"}
-$N_\text{4.3 ... 5.0}  \ =  \ $ { 81 3% }
+$N_\text{4.3 ... 5.0}  \ = \ $ { 81 3% }
-{Legen Sie die Punkte/Noten&ndash;Zuordnung fest.&nbsp; Ab wann bekommt man eine „3.0“?&nbsp; Wieviele Pr&uuml;fungsteilnehmer werden diese Note erhalten?
+{Specify the points/grades&ndash;assignment.&nbsp; At what point do you get a "3.0"?&nbsp; How many examinees will get this grade?
 |type="{}"}
-$N_\text{3.0} \ =  \ $ { 159 3% }
+$N_\text{3.0} \ = \ $ { 159 3% }
-{Wieviele Teilnehmer erhalten voraussichtlich die Note „2.7“?&nbsp; Begründen Sie, warum genau so viele Prüflinge die Note „3.3“ bekommen werden.
+{How many examinees are expected to receive the grade "2.7"?&nbsp; Justify why exactly that many examinees will receive the grade "3.3".
 |type="{}"}
-$N_\text{2.7}  \ =  \ $ { 146 3% }
+$N_\text{2.7}  \ = \ $ { 146 3% }
-{Welche Mittelnote wird sich bei dieser Pr&uuml;fung ergeben?&nbsp; Ber&uuml;cksichtigen Sie zur L&ouml;sung dieser Teilaufgabe das Ergebnis von  Teilaufgabe&nbsp; '''(5)'''.
+{What will be the mean grade on this exam?&nbsp; Consider the result of subtask&nbsp; '''(5)''' to solve this subtask.
 |type="{}"}
-$\rm Mittelnote \ =  \ $ { 3 3% }
+$\rm mean grade \ = \ $ { 3 3% }
 </quiz>
-===Musterlösung===
+===Solution===
 {{ML-Kopf}}
 '''(1)'''&nbsp;  Richtig sind <u>die Lösungsvorschläge 1 und 3</u>:

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−	[[Category:Theory of Stochastic Signals: Exercises\|^3.5 ~~Gaußverteilte Zufallsgröße~~^]]	+	[[Category:Theory of Stochastic Signals: Exercises\|^3.5 Gaussian Random Variable^]]

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