Problem
Let $X \sim \text{Uniform}(0,1)$.
Let $a, b$ be constants satisfying $0 < a < b < 1$.
Let $Y=1 (0 < X < b)$.
Let $Z=1 (a < X < 1)$.
(a) Are $X$ and $Y$ independent?
(b) Find $E(Y \vert Z)$.
Solution
Sources
- 36-700 hw4 problem 4
Let $X \sim \text{Uniform}(0,1)$.
Let $a, b$ be constants satisfying $0 < a < b < 1$.
Let $Y=1 (0 < X < b)$.
Let $Z=1 (a < X < 1)$.
(a) Are $X$ and $Y$ independent?
(b) Find $E(Y \vert Z)$.