Truncated Uniform Density. Let x be a uniformly distributed random variable with density f(x) =

1 2

for − 1 < x < 1

(a) What is the density function of f (x/x > −1/2)? Hint: Use the definition of a conditional density f (x/x > −1/2) = f(x)/Pr[x > −1/2] for − 1 2 < x < 1.

(b) What is the conditional mean E(x/x > −1/2)? How does it compare with the unconditional mean of x? Note that because we truncated the density from below, the new mean should shift to the right.

(c) What is the conditional variance var(x/x > −1/2)? How does it compare to the unconditional var(x)? (Truncation reduces the variance).