Question

on 5: Consider the joint probability density function of continuous random variables $x$ and $y$: $f(x,y) = \begin{cases} kxy^2, & 0 < x < 2, 0 < y < 1 \\ 0, & \text{Otherwise} \end{cases}$ a) Find the value of $k$ b) Find the marginal probability density functions of $x$ and $y$ c) Find an expression for the conditional probability density function $f_x(x|y)$ for $0 < y < 1$.

          on 5:
Consider the joint probability density function of
continuous random variables $x$ and $y$:
$f(x,y) = \begin{cases} kxy^2, & 0 < x < 2, 0 < y < 1 \\ 0, & \text{Otherwise} \end{cases}$
a) Find the value of $k$
b) Find the marginal probability density functions
of $x$ and $y$
c) Find an expression for the conditional probability
density function $f_x(x|y)$ for $0 < y < 1$.

on 5:
Consider the joint probability density function of
continuous random variables x and y:
f(x,y) = kxy^2, 0 < x < 2, 0 < y < 1
0, Otherwise
a) Find the value of k
b) Find the marginal probability density functions
of x and y
c) Find an expression for the conditional probability
density function fx(x|y) for 0 < y < 1.

Added by Adam L.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Ameer Said

02/24/2022

Step 1

\\ 0, & Otherwise \end{cases}$$ To find the value of k, we need to use the fact that the integral of the joint probability density function over the entire sample space must be equal to 1. $$\int_{0}^{1} \int_{0}^{2} kxy^2 dx dy = 1$$ Show more…

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on 5: Consider the joint probability density Function of continuous random Variables x and y: $$f(x,y) = \begin{cases} kxy^2, & 0<x<2, 0<y<1. \\ 0, & Otherwise \end{cases}$$ a) Find the value of k b) Find the Marginal Probability density functions x and y c) Find an Expression for the conditional probability density function for f(x|y) for 0<y<1.