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 ).

a. The mean of is

Recall that the variance of a random variable is

We have

so that

and the standard deviation is

b.

5x+40

5(x + 8)

7x - 49

7(x - 7)

18x + 9

9(2x + 1)

15x - 10

5(3x - 2)

step-by-step explanation:

for number one all you have to do is factor 5 out of 5x + 40

for number 2 factor 7 out of 7x - 49

for number three factor 9 out of 18x + 9

for number four factor 5 out of 15x - 10

answer: on graphs, the open and closed circles, or vertical asymptotes drawn as dashed lines us identify discontinuities.

as before, graphs and tables allow us to estimate at best.

when working with formulas, getting zero in the denominator indicates a point of discontinuity.

when working with piecewise-defined functions, check for discontinuities at the transition points where one piece ends and the next begins.

step-by-step explanation: