The density of random variable X is f(x) =4x³

625

for 0x5 and 0 otherwise. Do computations using the R integrate function.

a) Find the probability that X > 4

b) Find the probability that 3.5 < X < 4.5

c) Find the expected value of X

d) Find the variance of X

e) Find the standard deviation of X

f) Find the probability that X is within 1.2 standard deviations of its expected value

g) In the following paste your R script for this problem