Let X have probability density function f(x) = c/x for 1 0, and ln 1 = 0.) ...

---

Let X have probability density function f(x) = c/x for 1 <= x <= n, and f(x) = 0 otherwise, where n > 1 is a constant. (a) For what value of c is f(x) a valid probability density function? (b) Find the expected value E(X) and the variance Var(X) of X. (c) Find the 50th percentile of X. (Hint: use that exp(ln z) = z for z > 0, and ln 1 = 0.)