A bag contains five blue balls and three red balls A man dra

A bag contains five blue balls and three red balls. A man draws one ball at a time from the bag for three times without replacement. Let X denote the number of the red balls he drew from the bag. Find (a) the pdf of the r.v. X; (b) the CDF of X; (c) E[X]; (d) Var[X].

Solution

Total balls = 8

Blue ball = 5 and red ball = 3

Without replacement

X - No of red balls

X is binomial with n = 3 and p = 3/8 = 0.375

X can take values as 0,1,2,3

PDF of x and CDF of x are:

E(X) = np = 3(0.375) = 1.125

Var(X) = npq = 1.125(1-0.375)

= 0.703125