Question

Example The joint density function of X and Y is given by $$f(x, y) = \begin{cases} kxy & \text{if } x > 0, y > 0, x + y \le 1 \\ 0 & \text{otherwise} \end{cases}$$ Compute k. Ans. k = 24. Find the marginal pdf of X. Ans. $$f_x(x) = 12x(1-x)^2, 0 \le x \le 1$$. Find the marginal pdf of Y. Ans. $$f_y(y) = 12y(1 - y)^2, 0 \le y \le 1$$. Find E(X), E(Y), Var(X), and Var(Y).

Name: example the joint density function of x and y is given by fx y begincases kxy textif x 0 y 0 x y le 1 0 textotherwise endcases compute k ans k 24 find the marginal pdf of x ans fxx 12x1 x2 63934
Uploaded: 2022-03-06T05:12:33-08:00
Duration: 2 min 27 s
Channel: Ameer Said
Description: example the joint density function of x and y is given by fx y begincases kxy textif x 0 y 0 x y le 1 0 textotherwise endcases compute k ans k 24 find the marginal pdf of x ans fxx 12x1 x2 63934

          Example
The joint density function of X and Y is given by
$$f(x, y) = \begin{cases}
kxy & \text{if } x > 0, y > 0, x + y \le 1 \\
0 & \text{otherwise}
\end{cases}$$
Compute k. Ans. k = 24.
Find the marginal pdf of X. Ans. $$f_x(x) = 12x(1-x)^2, 0 \le x \le 1$$.
Find the marginal pdf of Y. Ans. $$f_y(y) = 12y(1 - y)^2, 0 \le y \le 1$$.
Find E(X), E(Y), Var(X), and Var(Y).

example the joint density function of x and y is given by fx y begincases kxy textif x 0 y 0 x y le 1 0 textotherwise endcases compute k ans k 24 find the marginal pdf of x ans fxx 12x1 x2 63934

Added by Brooke M.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Ameer Said

03/06/2022

Step 1

Step 1: The joint density function of X and Y is given by $$f(x, y) = \begin{cases} kxy & \text{if } x > 0, y > 0, x + y \le 1 \\ 0 & \text{otherwise} \end{cases}$$ We need to find the value of k. Show more…

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Example The joint density function of X and Y is given by $$f(x, y) = \begin{cases} kxy & \text{if } x > 0, y > 0, x + y \le 1 \\ 0 & \text{otherwise} \end{cases}$$ Compute k. Ans. k = 24. Find the marginal pdf of X. Ans. $$f_x(x) = 12x(1-x)^2, 0 \le x \le 1$$. Find the marginal pdf of Y. Ans. $$f_y(y) = 12y(1 - y)^2, 0 \le y \le 1$$. Find E(X), E(Y), Var(X), and Var(Y).