Suppose that the probabilities of a customer purchasing 0, 1, or 2 books at a book store are 0.2 , 0.4 , and 0.4 , respectively. what is the expected number of books a customer will purchase? the standard deviation of the customer's book purchases is

Porobability distribution of X

x P (x)

0 0.2

1 0.4

2 0.4

Total. 1.0

i] Expectation

Mean=Σxp

Variance=x²p - (∑xp) ²

thus:

Mean = (0*0.2) + (1*0.4) + (2*0.4)

=0+0.4+0.8

=1.2

ii] Variance

Variance=[ (0²*0.2) + (1²*0.4) + (2²*0.4) ] - (1.2) ²

=[0+0.4+1.6]-1.44

=0.56

hence:

standard deviation=sqrt (0.56) = 0.74833