please provide explanation for study purposes 1.

(10 points) Suppose for a given week, the proportion of time you spend playing games instead of studying for a certain exam involving statistics is modeled by the pdf f(x) = 0 else (a) What is the probability you spend half of your time playing games? (2 points) (b) What is the probability that you will spend between 35% and 77% of your time gaming it up? (2 points) (c) What is the expected proportion of time you will spend gaming? (3 points) (d) What is the variance of the proportion of time you will spend playing games? (3 points)(10 points) Consider a continuous random variable X with CDF if r 1 (a) Using only the CDF for X, compute the probability that X exceeds }. (2 points) (b) Determine the pdf of X. (2 points) (c) What is the expected value of X? (3 points) (d) What is the variance of X? (3 points)