A student estimates that the amount of time needed to solve a homework problem is exponentially distributed and is independent of the amount of time needed to solve any other homework problem. On average it takes the student 10 minutes to solve a homework problem. Thus, if X is the amount of time (in minutes) it takes a student to solve a homework problem, the density of X is: f(x,2) = 1 e¬Ax for 0 s xso, à = 1 where A is what R calls rate. 10 Hint: This is a problem involving the exponential distribution. If you can determine the parameter A for the distribution(given) then you should be able to easily answer parts a ,b ,c and use the built-in R functions for the exponential distribution (dexp(), pexp(), qexp()) for other parts . Or (not recommended) you should be able to use the R integrate command with f(x) defined as above or with dexp(). a) What is the expected value of X? 10 b) What is the variance of X? 100 c) What is the standard deviation of X? 10 d) What is the probability that X is larger than its expected value? 0.368 e) What is the probability that X is > 11? 0.333 f) What is the probability that X is > 12? 0.301 g) What is the probability that X > 12 given that X > 11? h) Calculate the 70th percentile of X.