2. [1/6 Points] DETAILS PREVIOUS ANSWERS The probability density function of random variable X is f(x) = sin(x) for 0 x and 0 otherwise. Do computations using the R integrate function. 2 a) Find the probability that X > 0.5 0.9563 b) Find the probability that 0.3 < x < 1.63 0.6839 c) Find the expected value of X 1.5708 d) Find the variance of X 0.2712 e) Find the standard deviation of X 0.5207 f) Find the probability that X is within 0.75 standard deviations of its expected value 0.5837 g) In the following paste your R script for this problem #a. Find the probability that x>0.5 prob_a