Let c, 1 ER and consider cx Sca-1, x € (1,00) fc(a) = LE = 0, o/w. (a) Determine c* E R such that fc* is a pdf for any 1 > 1. (b) Compute the cdf associated with fc*. (c) Compute P(2 < X < 5) and P(X > 4) for a random variable X with pdf fe* and 1 = 2. a (d) For which values of > 1 do expected value and variance of a random variable with pdf fc* exist? Compute the expected value and variance for these > 1.
