MHT CET202012 Oct 2020Evening ShiftMathematicsProbabilityActual
The p.d.f. of a random variable X is given by f(x)= k x if 0 x 4=0 otherwise, then P (1 < X < 4)=
Options
- A1 2
- B1 3
- C1 5
- D3 4
Correct answer
A. 1 2
Step-by-step solution
Given f ( x )= K x , if 0 x 4 =0, otherwise ₀⁴ K x dx =1 K [ x ^ 1 2 ( 1 2 ) ]₀⁴=1 2 ~K ( 4 -0)=1 4 ~K =1 K = 1 4 P (1 < x < 4)= ₁⁴ [ ( 1 4 ) x ) dx = 1 4 ₁⁴ x ^ - 1 2 dx = 1 4 [ x ^ 1 2 ( 1 2 ) ]₁⁴= 2 4 [4^ 1 2 -1 ]= 1 2 (2-1)= 1 2