(Solved):   please help with the whole question 4 4. (i) Let X be an exponential random variable with ...

 

please help with the whole question 4

4. (i) Let X be an exponential random variable with mean n?. Find and identify the distribution of Y = x2 [4] (ii) Find the probability density function for yn = max {X1, X2, ..., Xn} if a random sample X1, X2, ..., Xn is from the population with density: o f(x) = x2 x>?, ? >0 (iii) Let X be a random variable with probability density function f(x) = 0x0-1, 0 0 Find the probability density function of U = -lnx. [4] (iv) Let X, and X2 be independent exponential random variables, both with mean 0 > 0. (i) Find the probability density function of XIX Y = X1 + X2 [6] Find the probability that the random variable X, does not exceed the random variable 2X1 [3] (ii)