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Question

If m and σ2 are the mean and variance of variable X, whose distribution is given by:

X0123
P(X)1312016

Then:


A

m=σ2=2

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B

m=1,σ2=2

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C

m=σ2=1

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D

m=2,σ2=1

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Solution

The correct option is C

m=σ2=1


Explanation for the correct option:

Step 1: Solve for the mean

For the given probability distribution, the mean is given as

m=i=03Pixi

m=0×13+1×12+2×0+3×16

m=1

Step 2: Solve for the variance

The variance is given as

σ2=i=03Pixi-m2

σ2=130-12+121-12+02-12+163-12

σ2=13+23

σ2=1

Thus the value of m=σ2=1.

Hence option(C) is the correct answer.


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