Popper7&8 I'm struggling really hard, I need step by step on how you get the numbers to the answer

POPPER 7 The random variable X has probability density function: f (x) = {C - 2x 05x51 otherwise 1) What is the value of C? A) 1 B) 2 C ) 3 D) 4 E ) 5 C ( 1) - 1 = 1 0 / C : 2 2) What is E[X]? A) 0 B) 1/2 = 5 x ( 2 - 2 x ) dx C) 1/3 = 7 = 0.33 3 D) 2/3 [ x- To - 3 [ x ) . = 1 - 3 E) None of the above. 3) What is the third quartile of X? A) 1/2 B) 5/8 C) 3/4 D) 3/2 E) None of the above. Popper 8 1) The random variable X has cumulative distribution function: - o * 3 The random variable Y=12X+4 when X20 and Y=0 if X is negative. Find E[Y]. NOTE: F( x) - Subtracting f( x ) - Adding 12 :1 4 6 :3 2 S [ 1 + ] ] B) 4 4 -2 2 - 2 192 C) 11 [ 2 + 2 WHY DOES IT CONVERT TO THIS ? D) 24 = 9+2 LI E) 66 3.3 = 9 F) None of the above. 2 131 =2