Here is a probability density function with random variable X.

p(x) = { a(4-x²) for -2

{ 0 otherwise

A: Find a so that p(x) is a valid probability density function

• 0.667
• 0.111
• 0.250
• 0.750
• 0.500

B: Find p(x<=0)

• 0.667
• 0.750
• 0.500
• 0.250
• 0.593

C: Find E[X]

• 0
• 0.50
• -0.25
• -0.33
• -0.50

D: Find the variance of random variable Y, Y=2X+5

• 0.80
• 2.15
• 1.00
• 0.54
• 0.40