Ga random variable x has a probability density function fx(x) = ? 0.5 sin(x) , 0 ≤ x ≤ π 0 , otherwise another random variable y is defined as y = x + (x − π/2)3 . (a) what are the mean (expected value), variance and standard deviation of x? (b) plot the function y = y (x). what are the minimum and maximum possible values of y ? (c) from the plot, using only graphical thinking and no equations, what is the shape of the probability density function of y (i. e., fy ( specifically, how is the shape compared to that of fx(x)? (d) from the plot, using only graphical thinking and no equations, estimate (guess) the expected value and standard deviation of y (i. e., µy and σy ).