Ga random variable x has a probability density function fx(x) = ? 0 0: 5 sin(x) ; ; 0otherwise ≤ x ≤ π 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 ).

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)

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:

central angle of a triangle has the same measure as its intercepted arc.

step-by-step explanation: