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Q.

If m and σ2 are the mean and variance of the random variable X whose distributions given by: X=x                  :           0          1           2           3 P(X=x)            :          1/3       1/2         0         1/6

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a

m=σ2=2

b

m=1,σ2=2

c

m=σ2=1

d

m=2,σ2=1

answer is C.

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Detailed Solution

m=∑xP(X=x)=0(1/3)+1(1/2)+2(0)+3(1/6)=0+1/2+0+1/2=1 σ2=∑x2P(X=x)−m2=02(1/3)+12(1/2)+22(0)+32(1/6)−12 =0+1/2+0+3/2−1=2−1=1
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