Question

1. The sociologist surveyed the households in a small town. The random variable X represents the number of dependent children in the households. The following is the probability distribution of X:
X 0 1 2 3 4
P(X) 0.07 0.20 0.38 k 0.13
(a) Find the missing probability value of k
(b) Find the mean of X
(c) Find the standard deviation of X

Answer 1

a)k=1-(0.07+0.20+0.38+0.13)=0.22
b)M(X)=0*0.07+1*0.20+2*0.38+3*0.22+4*0.13=
=2.14
c)M(X^2)=0*0.07+1*0.20+4*0.38+9*0.22+
+16*0.13=5.78
The standard deviation=
=sqrt(M(X^2)-M(X)^2)=1.10