The p.d.f of a random variable x is given by `f(x)=(1)/(4a), 0 lt x lt 4a, (a gt 0)`
`=0,` otherwise
and `P(x lt (3a)/(2))=kP(xgt(5a)/(2)` then k= . . .

Options

A. 1
B. `(1)/(4)`
C. `(1)/(8)`
D. `(1)/(2)`

Answer

A

Explanation

We have p.d.f of a random variable x is given by
`f(x) = (1)/(4a), 0 lt x lt 4a. (a gt 0)`
and also, `p(x lt (3a)/(2)) = kp (x gt (5a)/(2))`
`implies int_(0)^((3a)/(2)) f(x) dx = k int_((5a)/(2))^(4a) f(x) dx`
`implies int_(0)^((3a)/(2)) ((1)/(4a)) dx = k int_((5a)/(2))^(4a) ((1)/(4a)) dx`
`implies (1)/(4a) int_(0)^((3a)/(2)) dx = (k)/(4a) int_((5a)/(2))^(4a) dx`
`implies (x)_(0)^((3a)/(2)) = k (x)_((5a)/(2))^(4a)`