Aufgaben:Exercise 2.7Z: C Program "z3"

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C program  $z3$  for generating
a binomial distribution

The C program  $z3$  given opposite successively generates a binomially distributed random variable with the characteristic variables  $I$  and  $p$. 

• It uses the program  $z1$ already described and analyzed in  Exercise 2.7 .
• Assume that the program is called with parameters  $I = 4$  and  $p = 0.75$ .
• The first eight real-valued numbers  (all between zero and one)  generated by the random generator  $\text{random()}$  are:

$$\rm 0.75, \ 0.19, \ 0.43, \ 0.08, \ 0.99, \ 0.32, \ 0.53, \ 0.02.$$

Hints:

• The exercise belongs to the chapter  Generation of Discrete Random Variables.
• Reference is also made to the chapter  binomial distribution.

Questions

1 Which of the following statements are true?

	$z3$  returns a binomially distributed random variable, because several binary values are summed up.
	To pass parameters to the program $z1$, the array  $\text{p_array} = \big [1-p, \ \ p \big]$  is used.
	Passing of  $M=2$  must be done with "$\rm 2L$", because  $z1$  expects a long (data type) value.

2 What value will be output on  first call  of  $z3$ ?

$z3 \ = \ $

3 What value will be output on  second call  of  $z3$ ?

$z3 \ = \ $

Solution

Solution

(1)  All three statements are true.

(2)  The real-valued random numbers  $0.75$,  $0.19$,  $0.43$  and  $0.08$  are each compared with  $0.25$  .

• This comparison results in the binary values  $1, \ 0, \ 1, \ 0$.
• This results in the sum  $\underline{z3 = 2}$ in the first call.

(3)  Analogous to the result of the subtask  (2)  the binary values  $1, \ 1, \ 1, \ 0$  now occur because of the random values  $0.99$,  $0.32$,  $0.53$  and  $0.02$  .

• This leads to the output value  $\underline{z3 = 3}$  (again sum of binary values).