A random variable X can attain only the value 1,2,3,4,5 with respective probabilities k,2k,3k,2k,k. if m is the mean of the probability distribution, then (k,m) is equal to

Options

A. `(3,(1)/(9))`
B. `((1)/(9),3)`
C. `((1)/(8),4)`
D. `(1,3)`

Answer

B

Explanation

We know sum of probability distribution is 1.
`thereforex+2k+3k+2k+k=1impliesk=(1)/(9)`
`therefore`Mean, `m=underset(i=1)overset(5)(sum)p_(i)x_(i)`
`=k(1)+2k(2)+3k(3)+2k(4)+k(5)`
`=k(1+4+9+8+5)=(1)/(9)xx27=3`
`therefore(k,m)=((1)/(9),3)`