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.

option c) graph of line going through 1, 4 and 3, 10

step-by-step explanation:

let y equal to margo's coin collection

let x equal to number of years

at the begining x=0, y=1 → point=(x,y)→point=(0,1)

she adds 3 coins per year, then y=1+3x

at x=1, y=1+3(1)=1+3→y=4→point=(x,y)→point=(1,4)

at x=3, y=1+3(3)=1+9→y=10→point=(x,y)→point=(3,10)

the graph of line going through (1, 4) and (3, 10), then the option c is the correct.