Let x have the uniform distribution u(0, 2) and let the conditional distribution of y , given that x = x, be u(0, x). find the joint p. d.f. f(x, y) of x and y , and be sure to state the domain of f(x, y). find e(y |x)

Step-by-step explanation:

We have two random variables X and Y. and given that X=x, Y has uniform distribution (0,x)

From the definition of the uniform distribution we have the densities for each random variable given by:

And on this case we can find the joint density with the following formula:

And multiplying the densities we got this:

Now with the joint density we can find the expected value E(Y|x) with the following formula:

And replacing we got:

no, the equation would be invalid since they are both not equal.

step-by-step explanation:

here you got

4y-6+4y 2-9

first, you would simplify the equation on the form.

4y-6+4y 2-9

then, move all the terms that contains a y to the left and all the other terms to the right.

+4y-4y+-9-6

finally, you will simplify the left and the right side of the equation.

y=-3