If X is a random variable with distribution given below
The value of k and its variance are

Options

A. `1//8,22//27`
B. `1//8,23//27`
C. `1//8,24//27`
D. `1//8,3//4`

Answer

D

Explanation

The given distribution is a probability distribution
`thereforeP(X=0)+P(X=1)+P(X=2)+P(X=3)=1`
`rArr" "k+3k+3k+k=1rArrk=1/8`
`therefore" ""Variance"=Sigmax^2P(x)-[SigmaxP(x)]^2`
`rArr" ""Variance"=(24)/8-((12)/8)^2=3-9/4=3/4`