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 = …….

Question

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 = ……., 1, 1 2, 1 8, 3 2

MARKS App · Accepted Answer

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

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