The life time (in hundred hours) Y of an electronic component is a random variable that has an approximately gamma distr

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The life time (in hundred hours) Y of an electronic component is
a random variable that has an approximately gamma distribution with
a mean of 1.25 hundred hours and a variance of 0.3125 (hundred hour
squared).

a. What is the pdf for the random variable Y?
b. What is the probability that the component will operate for more
than 2 hundred hours without failure? Please use R to
calculate.
c. Find the lift time so that 20% of the life time are longer than
it. Please use R to calculate.
d. If X = 5 Y 2, find E(X).