The joint density function of the random variables X and Y is f(x, y) = 6x 0 < x < 1, 0 < y < 1 − x

a. Show that X and Y are not independent.

b. Find f(x|y) and use it to find P(X > 0.3|Y = 0.5)

step-by-step explanation:

step 1: solve one of the equations for one of the variables. let's solve the first equation for y:

step 2: substitute that equation into the other equation, and solve for x.

step 3: substitute x = 4 x = 4 x=4 into one of the original equations, and solve for y.

mariah is studying the life cycle of the monarch butterfly. she must choose one stage in the cycle to present in science class: egg, caterpillar, chrysalis, or adult. she plans to make her choice randomly using a custom spinner divided into four sections. first, however, she spins the spinner 50 times to see the frequencies it generates.

stage times landed on

egg 10

caterpillar 12

chrysalis 15

adult 13

step-by-step explanation:

time is equal to distance over rate so

t = d/r

need a little bit more information for the second question.