A company has five warehouses only two of which have a parti

A company has five warehouses only two of which have a particular product in stock. A salesperson calls the five warehouses in random order until a warehouse with the product is reached. Let the random variable X be the number of calls made by the salesperson.

(a) Find P(X < 3)

(b) Find x = E(X)

(c) Find x^ 2 = V(X)

Solution

Binomial Distribution

PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial

a)
P( X < 3) = P(X=2) + P(X=1) + P(X=0)
= ( 5 2 ) * 0.4^2 * ( 1- 0.4 ) ^3 + ( 5 1 ) * 0.4^1 * ( 1- 0.4 ) ^4 + ( 5 0 ) * 0.4^0 * ( 1- 0.4 ) ^5
= 0.6826
b)
Mean ( np ) =2
c)
Standard Deviation ( npq )= 5*0.4*0.6 = 1.0954
Variance = 5*0.4*0.6 = 1.2