Question

an urn contain 5 red and 2 black balls , two balls are randomly drawn without replacement . let x represent number of black ball draw .what are the possible value of x ? In x a random variable ? If yes, find the mean and variance of x?

Answer 1

In the attachment I have answered
this problem.

Steps are very easy to understand.

I hope this answer help you

Answer 2

Answer:

X is a random variable.

Step-by-step explanation:

Given : An urn contain 5 red and 2 black balls, two balls are randomly drawn without replacement. Let x represent number of black ball draw.

To find : What are the possible value of x?

Solution :

An urn contain 5 red and 2 black balls.

The number of ways in which two balls can be represented are

{(RR), (RB), (BR), (BB)}

Let X represent the number of black balls. Possible values of X are:

X(RR) = 0, X(RB) = 1, X(BR = 1) and X (BB) = 2.

Therefore the possible values of X are 0, 1 and 2.

$P(X=0)=\frac{1}{4}$

$P(X=1)=\frac{2}{4}$

$P(X=2)=\frac{1}{4}$

$\sum X_i=P(X=0)+P(X=1)+P(X=2)$

$\sum X_i=\frac{1}{4}+\frac{2}{4}+\frac{1}{4}$

$\sum X_i=\frac{4}{4}$

$\sum X_i=1$

Therefore,  X is a random variable.