Question

Let X and Y be independent random variables uniformly distributed in the interval (0, 1). In the followings provide complete derivations and explanation of results. a) Find the expectation E[X + Y] b) Find the conditional PDF of X given X > Y. c) Find the conditional PDF of Y given X > Y. d) Find the conditional expectation E[X + Y|X > Y]. e) Find the conditional PDF of Y/X given X > Y.

          Let X and Y be independent random variables uniformly distributed in the interval (0, 1).
In the followings provide complete derivations and explanation of results.
a) Find the expectation E[X + Y]
b) Find the conditional PDF of X given X > Y.
c) Find the conditional PDF of Y given X > Y.
d) Find the conditional expectation E[X + Y|X > Y].
e) Find the conditional PDF of Y/X given X > Y.

Let X and Y be independent random variables uniformly distributed in the interval (0, 1).
In the followings provide complete derivations and explanation of results.
a) Find the expectation E[X + Y]
b) Find the conditional PDF of X given X > Y.
c) Find the conditional PDF of Y given X > Y.
d) Find the conditional expectation E[X + Y|X > Y].
e) Find the conditional PDF of Y/X given X > Y.

Added by Teresa -.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Farruh Turgunov

Step 1

Since X and Y are uniformly distributed in the interval (0, 1), their expectations are: E[X] = E[Y] = \int_0^1 x dx = \frac{1}{2} So, E[X + Y] = E[X] + E[Y] = \frac{1}{2} + \frac{1}{2} = 1. Thus, the expectation E[X + Y] is: $\boxed{E[X + Y] = 1}$ b) Show more…

Show all steps

Thanks for your feedback!

Let X and Y be independent random variables uniformly distributed in the interval (0, 1). In the following, provide complete derivations and explanations of the results. a) Find the expectation E[X + Y]. b) Find the conditional PDF of X given X > Y. c) Find the conditional PDF of Y given X > Y. d) Find the conditional expectation E[X + Y | X > Y]. e) Find the conditional PDF of Y/X given X > Y.