Suppose FY (y) = y3 for 0 ≤ y < 1/2, and FY (y) = 1...

Question

Question

Suppose FY (y) = y³ for 0 ≤ y < 1/2, and FY (y) = 1 − (1-y)³ for 1/2 ≤ y ≤ 1. Compute each of the following.

(a) P(1/3 < Y < 3/4)

(b) P(Y = 1/3)

(c) P(Y = 1/2)

math Statistics-And-Probability

Answer 1

Answer #1

a)P(1/3<Y<3/4)=F(3/4)-F(1/3) =(1-(1-3/4)³)-(1/3)³ =63/64-1/27 =0.947338

b)P(Y=1/3) =0 (as point probability on a continuous distribution is 0)

c)P(Y=1/2)=P(Y<=2)-P(Y<2) =(1-(1/2)³)-(1/2)³ =(7/8)-(1/8)=6/8=3/4=0.75

Answer 2

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