If the probability distribution of a random variable X is as given below
Then, mean and variance are

Options

A. `4/5 and (54)/(25)`
B. `4/(10) and (54)/(25)`
C. `4/(15) and (27)/(25)`
D. None of these

Answer

A

Explanation

The given distribution is a probability distribution
`thereforeP(x=-2)+P(x=-1)+P(x=0)+P(x=1)+P(x=2)+P(x=3)=1`
`rArr" "1/(10)+k+1/5+2k+3/(10)+k=1`
`" "4k=4/(10)`
`rArr" "k=1/(10)`
Mean `=1/(10)-(-2)+k(-1)+1/5(0)+2k(1)+3/(10)(2)+k(3)`
`=-2/(10)-k+0+2k+6/(10)+3k`
`=4/(10)+4k=4/(10)+4xx1/(10)`
`=8/(10)=4/5`
Variance `=1/(10)(-2)^2+k(-1)^2+1/5(0)^2+2k(1)^2+3/(10)(2)^2+k(3)^2-("mean")^2`
`=4/(10)+k+0+2k+(12)/(10)+9k-(4/5)^2`
`=(16)/(10)+12k-(16)/(25)=(16)/(25)+12xx1/(10)-(16)/(25)=(54)/(25)`