Question

A continuous random variable X has probability density function

f(x) = a for −2 < x < 0

bx for 0 < x ≤ 1  

0 otherwise

where a and b are constants. It is known that E(X) = 0.

(a) Determine a and b.

(b) Find Var(X)

(c) Find the median of X, i.e. a number m such that P(X ≤ m) = 1/2

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