Question

Let X and Y be two jointly continuous random variables with joint pdf $$f_{X,Y}(x,y) = \begin{cases} cx^2y & 0 \le y \le x \le 1 \\ 0 & \text{otherwise} \end{cases}$$ a) Find the constant c b) Find the marginal pdfs $f_X(x)$ and $f_Y(y)$ c) Find $P(Y \le \frac{1}{4} | Y \le \frac{1}{2})$ d) Find $P(Y \le \frac{x}{2})$

Name: let x and y be two jointly continuous random variables with joint pdf fxyxy begincases cx2y 0 le y le x le 1 0 textotherwise endcases a find the constant c b find the marginal pdfs fxx and 32909
Uploaded: 2022-02-07T09:19:59-08:00
Duration: 4 min 10 s
Channel: Rahi P
Description: let x and y be two jointly continuous random variables with joint pdf fxyxy begincases cx2y 0 le y le x le 1 0 textotherwise endcases a find the constant c b find the marginal pdfs fxx and 32909

          Let X and Y be two jointly continuous random variables with joint pdf
$$f_{X,Y}(x,y) = \begin{cases}
cx^2y & 0 \le y \le x \le 1 \\
0 & \text{otherwise}
\end{cases}$$
a) Find the constant c
b) Find the marginal pdfs $f_X(x)$ and $f_Y(y)$
c) Find $P(Y \le \frac{1}{4} | Y \le \frac{1}{2})$
d) Find $P(Y \le \frac{x}{2})$

let x and y be two jointly continuous random variables with joint pdf fxyxy begincases cx2y 0 le y le x le 1 0 textotherwise endcases a find the constant c b find the marginal pdfs fxx and 32909

Added by Alyssa O.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Rahi P

02/07/2022

Step 1

Step 1: To find the constant c, we use the fact that the integral of the joint pdf over the entire support must equal 1. Show more…

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Let X and Y be two jointly continuous random variables with joint pdf $$f_{X,Y}(x,y) = \begin{cases} cx^2y & 0 \le y \le x \le 1 \\ 0 & \text{otherwise} \end{cases}$$ a) Find the constant c b) Find the marginal pdfs $f_X(x)$ and $f_Y(y)$ c) Find $P(Y \le \frac{1}{4} | Y \le \frac{1}{2})$ d) Find $P(Y \le \frac{x}{2})$