Aufgaben:Exercise 1.1: Entropy of the Weather - Revision history

Guenter at 11:59, 10 August 2021

2021-08-10T11:59:33Z

2021-06-30T11:35:41Z

2021-06-16T14:13:08Z

2021-06-16T14:08:17Z

2021-06-15T13:05:10Z

2021-06-01T12:17:30Z

2021-05-28T14:41:12Z

Text replacement - "”" to """

2021-05-28T14:40:30Z

Text replacement - "„" to """

2021-05-28T14:23:38Z

2021-05-28T12:46:58Z

← Older revision		Revision as of 11:59, 10 August 2021
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−	{{quiz-Header\|Buchseite=~~Informationstheorie~~/~~Gedächtnislose Nachrichtenquellen~~	+	{{quiz-Header\|Buchseite=Information_Theory/Discrete_Memoryless_Sources
	}}		}}

@@ Line 3: / Line 3: @@
 }}
-[[File:EN_Inf_A_1_1.png|right|frame|Five different binary sources]]
+[[File:EN_Inf_A_1_1_v2.png|right|frame|Five different binary sources]]
 A weather station queries different regions every day and receives a message&nbsp;  $x$&nbsp; back as a response in each case, namely

@@ Line 116: / Line 116: @@
   \hspace{0.15cm}
 \underline {= 0.211\,{\rm bit/enquiry}}\hspace{0.05cm}.$$
-*Although&nbsp; (more precisely:&nbsp; because)&nbsp; event&nbsp; $\rm B$&nbsp; occurs less frequently than&nbsp; $\rm G$, its contribution to entropy is greater.
+*Although&nbsp; (more precisely:&nbsp; because)&nbsp; event&nbsp; $\rm B$&nbsp; occurs less frequently than&nbsp; $\rm G$, its contribution to entropy is much greater.
 '''(6)'''&nbsp; Statements <u>1 and 3</u> are correct:
-*$\rm B$&nbsp; and&nbsp; $\rm G$&nbsp; are indeed equally probable in the&nbsp; "unknown"&nbsp; file: &nbsp; the&nbsp; $60$&nbsp; symbols shown divide into&nbsp;   $30$&nbsp;times&nbsp; $\rm B$&nbsp; and&nbsp; $30$&nbsp;times&nbsp; $\rm G$.
+*$\rm B$&nbsp; and&nbsp; $\rm G$&nbsp; are indeed equally probable in the&nbsp; "unknown"&nbsp; file: &nbsp; The&nbsp; $60$&nbsp; symbols shown divide into&nbsp;   $30$&nbsp;times&nbsp; $\rm B$&nbsp; and&nbsp; $30$&nbsp;times&nbsp; $\rm G$.
 *However, there are now strong statistical ties within the temporal sequence.&nbsp; Long periods of good weather are usually followed by many bad days in a row.
 *Because of this statistical dependence within the&nbsp; $\rm B/G$&nbsp; sequence&nbsp; $H_\text{U} = 0.722 \; \rm bit/enquiry$&nbsp; is smaller than&nbsp; $H_\text{M} = 1 \; \rm bit/enquiry$.

@@ Line 14: / Line 14: @@
 with the&nbsp; base-2 logarithm
-:$${\rm log}_2\hspace{0.1cm}p=\frac{{\rm lg}\hspace{0.1cm}p}{{\rm lg}\hspace{0.1cm}2}\hspace{0.3cm} \left ( =  {\rm ld}\hspace{0.1cm}p \right ) \hspace{0.05cm}.$$
+:$${\rm log}_2\hspace{0.1cm}p=\frac{{\rm lg}\hspace{0.1cm}p}{{\rm lg}\hspace{0.1cm}2}.$$
 Here,&nbsp; "lg"&nbsp; denotes the logarithm to the base&nbsp; $10$.&nbsp; It should also be mentioned that the pseudo-unit&nbsp; $\text{bit/enquiry}$ &nbsp;must be added in each case.
@@ Line 73: / Line 73: @@
-{Which statements could be true for the file&nbsp; "Unknown&"?
+{Which statements could be true for the file&nbsp; "Unknown"?
 |type="[]"}
 + Events&nbsp; $\rm B$&nbsp; and&nbsp; $\rm G$&nbsp; are approximately equally probable.

@@ Line 3: / Line 3: @@
 }}
-[[File:Inf_A_1_1_vers2.png|right|frame|Five different binary sources]]
+[[File:EN_Inf_A_1_1.png|right|frame|Five different binary sources]]
 A weather station queries different regions every day and receives a message&nbsp;  $x$&nbsp; back as a response in each case, namely

← Older revision		Revision as of 12:17, 1 June 2021
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	*For the first four files it is assumed that the events  $\rm B$  and  $\rm G$  are statistically independent, a rather unrealistic assumption for weather practice.		*For the first four files it is assumed that the events  $\rm B$  and  $\rm G$  are statistically independent, a rather unrealistic assumption for weather practice.

−	*The task was designed at a time when  [https://en.wikipedia.org/wiki/Greta_Thunberg Greta]  was just starting school.  We leave it to you to rename  "Paradise"  ~~tonbsp~~; "Hell".	+	*The task was designed at a time when  [https://en.wikipedia.org/wiki/Greta_Thunberg Greta]  was just starting school.  We leave it to you to rename  "Paradise"  to  "Hell".

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-{What is the entropy&nbsp; (that is:&nbsp; the average information content)&nbsp; $H_{\rm P}$&nbsp; of the file&nbsp; "paradise&rdquo;?&nbsp; Interpret the result.
+{What is the entropy&nbsp; (that is:&nbsp; the average information content)&nbsp; $H_{\rm P}$&nbsp; of the file&nbsp; "paradise"?&nbsp; Interpret the result.
 |type="{}"}
 $H_{\rm P}\ =  \ $ { 0.211 3% } $\ \rm bit/enquiry$

← Older revision		Revision as of 12:46, 28 May 2021
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	*For the first four files it is assumed that the events  $\rm B$  and  $\rm G$  are statistically independent, a rather unrealistic assumption for weather practice.		*For the first four files it is assumed that the events  $\rm B$  and  $\rm G$  are statistically independent, a rather unrealistic assumption for weather practice.

−	*The task was designed at a time when  [https://en.wikipedia.org/wiki/Greta_Thunberg Greta]  was just starting school.  We leave it to you to rename &~~bdquo~~;~~paradise” to~~ &~~bdquo~~;~~hell&rdquo~~;.	+	*The task was designed at a time when  [https://en.wikipedia.org/wiki/Greta_Thunberg Greta]  was just starting school.  We leave it to you to rename  "Paradise"  tonbsp; "Hell".