3. Problem 3: The weekly repair cost (in $100), X, for a certain machine has a probability density function given by f(x)=c(1-x), for 03x31 and f(x)=0 otherwise a- Find the value of c that makes f(x) a valid probability density function. b- Find and sketch the cumulative distribution function of X. c- What is the probability that repair costs will exceed $75 during a week? d- Find the mean and variance of the repair costs