1. (30 points) Let X be a random variable with Beta(a,b) distribution, that is 1 f (2 ) = Bla, b ) -20-1(1 -x)6-1 0 0. Compute the probability density function of the random variable Y = log(X), where log() is the natural logarithm. 3. (35 points) The time it takes an earthquake to hit a city is an exponentially distributed random variable with mean 15 (years). What is a) the probability that it will take more than 15 years for an earthquake to hit? b) the conditional probability that it takes at least 10 years, given that it has already taken 3 years