3. Let X and Y be two random variables withandfy(y):=fxy(x|y) =y²/3, if 0 ≤ y ≤10,otherwise,Find E[X].Give your answers to two decimal places.Sye-v², if x ≥ 00,otherwise.

Given information: fy=53y23, 0≤y≤1fx|y=ye-yx, x≥0 Consider, fx,y=fx|y*fy =ye-yx*53y23…

Answered: 3. Let X and Y be two random variables…

3. Let X and Y be two random variables with and fy(y) = 10, fxy(x|y) = 2/3, if 0 ≤ y ≤1 otherwise, ye-, if r 20 0. otherwise.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

3. Let X and Y be two random variables with
and
fy(y):
=
fxy(x|y) =
y²/3, if 0 ≤ y ≤1
0,
otherwise,
Find E[X].
Give your answers to two decimal places.
Sye-v², if x ≥ 0
0,
otherwise.

Expert Solution

Step 1

Given information:

$f (y) = \frac{5}{3} y^{\frac{2}{3}}, 0 \leq y \leq 1 f (x | y) = y e^{- y x}, x \geq 0$

Consider,

$f (x, y) = f (x | y) * f (y) = y e^{- y x} * \frac{5}{3} y^{\frac{2}{3}} = \frac{5}{3} y^{\frac{5}{3}} e^{- y x}, x \geq 0, 0 \leq y \leq 1$

Step by step

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