G Define two jointly distributed continuous random variables, X and Y, as the fluid velocities measured in meters/second at two different locations, A and B, respectively, in a pipe flow system. The marginal density function for X is . Additionally, the conditional density function is . i. Are X and Y independent? Justify your answer. ii. If the fluid velocity at location A is 0.5 m/s, determine the probability that location B has a fluid velocity that is less than the fluid velocity of location A. iii. Find the probability density function f(x, y). iv. Find the marginal density function h(y). v. Find the conditional density

Apsychology student wishes to investigate differences in political opinions between business majors and political science majors at her college. she randomly selects 100 students from the 260 business majors and 100 students from the 180 political science majors. does this sampling plan result in a simple random sample? why or why not? no, because each group of 200 students in the sample does not have the same chance of being selected. yes, because each group of 200 students in the sample has the same chance of being selected. no, because each individual student does not have an equal chance of being selected. yes, because each individual student has the same chance of being selected.

Aregular pentagon with a perimeter of 21 inches is dilated by a scale factor of 5/3 to create a new pentagon. what is the perimeter of the new pentagon?

What is the domain of the given function? {(3,-2), (6, 1), (-1, 4), (5,9), (-4, 0); o {x | x= -4,-1, 3, 5, 6} o {yl y = -2,0, 1,4,9} o {x|x = -4,-2, -1,0, 1, 3, 4, 5, 6, 9} o y y = 4,-2, -1, 0, 1, 3, 4, 5, 6, 9}