Let X be a random variable of the mixed type having the distribution function

F (x) = 0 where x < 0

F (x) = x ^ 2 / 4 where 0 x < 1

F (x) = x+1 / 4 where 1 x < 2

F (x) = 1 where x 2

Question 1: Find the mean of X

Question 2: Find the variance of X

Question 3: Find P(1/4 < X < 1)

Question 4: Find P(X = 1)

Question 5: Find P(X = 1/2)