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 ).

Darian wants to build a regulation size pool table that is 9 feet in length.he plans he ordered are 18 by 36 inches. what is the scale factor of the dilation he must use to build a regulation pool table

High school seniors with strong academic records apply to the nation’s most selective colleges in greater numbers each year. because the number of slots remains relatively stable, some colleges reject more early applicants. suppose that for a recent admissions class, an ivy league college received 2851 applications for early admission. of this group, it admitted 1033 students early, rejected 854 outright, and deferred 964 to the regular admission pool for further consideration. in the past, this school has admitted 18% of the deferred early admission applicants during the regular admission process. counting the students admitted early and the students admitted during the regular admission process, the total class size was 2375. let e, r, and d represent the events that a student who applies for early admission is admitted early, rejected outright, or deferred to the regular admissions pool.suppose a student applies for early admission. what is the probability that the student will be admitted for early admission or be deferred and later admitted during the regular admission process?

5. which description does not guarantee that a quadrilateral is a squar ajo is a parallelogram with perpendicular diagonals 0% has all sides congruent and all angles congruent o has all right angles and has all sides congruent 10% is both a rectangle and a rhombus 30%