MHT CET2019Evening ShiftMathematicsProbabilityActual
The p. d. f. of a random variable x is given by f x = 1 4 a , 0 < x < 4 a , a > 0 =0, otherwise and P x < 3 a 2 = k P x > 5 a 2 then K = …….
Options
- A1
- B1 2
- C1 8
- D3 2
Correct answer
A. 1
Step-by-step solution
We have p. d. f. of a random variable x is given by f x = 1 4 a , 0 < x < 4 a . a > 0 and also, p x < 3 a 2 = k p x > 5 a 2 ⇒ ∫ 0 3 a 2 f x d x = k ∫ 5 a 2 4 a f x d x ⇒ ∫ 0 3 a 2 1 4 a d x = k ∫ 5 a 2 4 a 1 4 a d x ⇒ 1 4 a ∫ 0 3 a 2 d x = k 4 a ∫ 5 a 2 4 a d x ⇒ x 0 3 a 2 = k x 5 a 2 4 a ⇒ 3 a 2 - 0 = k 4 a - 5 a 2 ⇒ 3 a 2 = k 3 a 2 ⇒ k = 1