Question

An urn contains 15 red balls, 10 black balls and 25 white balls. 10 balls are randomly drawn.

We define random variables N as the number of black balls in the extraction and B as the number of white balls in the extraction.

a) Calculate the joint density function of N and B.

b) Calculate the joint distribution function of N and B.

Answer 1

The urn contains 15 red balls, 10 black balls and 25 white balls. 10 balls are randomly picked.

N - the number of black balls picked

B - the number of white balls picked

a) There are a total of balls. The number of ways of choosing 10 balls from 50 is .

The number of ways of choosing n black balls is

The number of ways of choosing b white balls is

The joint mass function of N and B is

b) The joint distribution function of N and B is

We cannot get a closed form expression for the above sum.