Let X and Y be a random variable with joint PDF: $f_{XY}(x, y) = \begin{cases} \frac{ay}{x^2}, & x \ge 1, 0 \le y \le 1 \\ 0 & \text{otherwise} \end{cases}$ 1. What is a? 2. What is the conditional PDF $f_{Y|X}(x|y)$ of Y given X = x? 3. What is the conditional expectation of Y given X? 4. What is the expected value of Y?

          Let X and Y be a random variable with joint PDF:
$f_{XY}(x, y) = \begin{cases} \frac{ay}{x^2}, & x \ge 1, 0 \le y \le 1 \\ 0 & \text{otherwise} \end{cases}$

1. What is a?
2. What is the conditional PDF $f_{Y|X}(x|y)$ of Y given
X = x?
3. What is the conditional expectation of Y given X?
4. What is the expected value of Y?

Let X and Y be a random variable with joint PDF:
fXY(x, y) = (ay)/(x^2), x ≥ 1, 0 ≤ y ≤ 1
0 otherwise

1. What is a?
2. What is the conditional PDF fY|X(x|y) of Y given
X = x?
3. What is the conditional expectation of Y given X?
4. What is the expected value of Y?

Added by Kevin S.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Oluwadamilola Ameobi

Step 1

To find the value of a, we need to integrate the joint PDF over its entire support, which is the region where 0 < y < 1. ∫∫ f(x,y) dx dy = 1 ∫∫ a*y^2 dx dy = 1 Since the joint PDF is constant over its support, we can take it out of the integral: a * ∫∫ y^2 dx Show more…

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Let X and Y be a random variable with joint PDF: ay 32 fxx (x,y) = 2 > 1,0 < y < 1 otherwise 1. What is a? 2. What is the conditional PDF fy x (wly) of Y given X = x? 3. What is the conditional expectation of Ygiven X? 4. What is the expected value of Y?