Question 5 (6 points) Function g(x) is defined defined as follows.
ſ 1. 9(x) = { 1 if r [0,1] ; 0, otherwise
Suppose that the pdf fx of random variable X is
fx(x) = 1/2s(x− 1) + 1/4 g(x − 2) + ag(x/2)
for some value a
1. Determine a.
2. Determine the cdf Fy of X.
3. Determine the conditional pdf of X given that X is less than 2.5.