4-44. Suppose that the probability density function for a continuous random variable X is f (x) = -1 2x−1/2 0 < x < 1;

0 elsewhere.

Does X have a symmetrical probability density function? (Hint: Compare E(X) and γ0.5, with the latter determined from P(X ≤ γ0.5) =

4 γ0.5

−∞ f (x)dx = 0.5.)