Question

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

Answer 1

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