g 3. Suppose X and Y are independent, Binomial random variables, respectively, with parameters (n1, p) and (n2, p). Calculate the frequency function of X Y .

Answer and Explanation:

Solution:

Let x and y are independent, ariables.

The parameters of x and y are (n1, p) and (n2, p), respectively.

It means the sum of the independent binomial variable is itself a binomial random variable.

Consider probability of the event [ x = n1],

Denoted by: p(x=n1)

The function:

                   P(n1) = p(x = n1)

Over the possible value of x say, n1, n2, n3, …, is called frequency function.

The frequency function must satisfy.

∑I p (ni) = 1,

Where the sum is possible values of x.

Similarly,

Consider probability of the event [ y = n2],

Denoted by: p(y=n2)

The function:

P (n2) = p(y = n2)

Over the possible value of y say, n1, n2, n3, …, is called frequency function.

The frequency function completely describes the probabilistic nature of the random variable.