Question

1. Let X be a standard uniform random variable, i.e., a random variable with probability density function

f(x)=1 \text { for } 0 \leq x \leq 1

0 otherwise

\text { a. Find } P\left[X \geq \frac{1}{2} \mid X \leq \frac{3}{4}\right] \text {. }

\text { b. Find the expected value and variance of } X \text { conditional on } X \leq \frac{3}{4} \text {. }

c. Find the distribution function and probability density function ofY2X – 1.