Let Y 1 and Y 2 have the joint probability density function given by f (y1,y2)= {ky1y2, 0, 0 ≤y1 ≤1,0≤ y2 ≤1, elsewhere. a) Find the value of k that makes this a probability density function.

Here’s how to approach this question For part (a), to find the probability that both machines are in operation for more than half an hour, set up the double integral of the given joint probability …

Math Statistics and Probability Statistics and Probability questions and answers 5.26 In Exercise 5.8, we derived the fact that f (y1,y2)= {4y1y2,0,0≤y1≤1,0≤y2≤1, elsewhere is a valid joint …

Math Statistics and Probability Statistics and Probability questions and answers Let Y1 and Y2 have the joint probability density function given by f (y1, y2) = k (1 − y2), 0 ≤ y1 ≤ y2 ≤ 1, 0, …

Statistics and Probability questions and answers 5.1.10 VS Determine the value of c that makes the function f (x,y) = ce-2x-3y a joint probability density function over the range 0 < x and x < y.

Determine the value of c such that the function f (x,y) = cxy for 0 < x <3 and 0 < y <3 satisfies the properties of a joint probability density function.

Consider two independent random variables X and Y with the joint probability density function: f X,Y (x,y)={e−(x+y) 0 for x>0,y>0 otherwise 1. Check if this joint probability distribution is …

To get started, recall that the marginal probability density function can be found by integrating the joint density function over the range of the other variable.

Statistics and Probability questions and answers 5.77 In Exercise 5.9, we determined that f (y1,y2)= {6 (1−y2),0,0≤y1≤y2≤1 elsewhere is a valid joint probability density function.

The random variables X and Y are independent if: the joint probability density function of (X,Y) is equal to the marginal probability density functions of X and Y. the joint probability density …