Exercise 2.7Z: C Program "z3"

C program $z3$ for generating
a binomial distribution

The C program $z3$ given here 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

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 $\underline{z3 = 2}$ for 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 the sum of binary values).

	$z3$ 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.