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:

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step-by-step explanation: