Answered: V and W are independent random…

V and W are independent random variables with the following density functions: Find the distribution function of random variable X = V + W

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

V and W are independent random variables with the following density functions:

Find the distribution function of random variable X = V + W

fv (v) =
J2v
lo
3w²
fw (w) = to
for 0 ≤v≤1
otherwise
for 0≤w<1
otherwise

Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.

Expert Solution

Step 1

Given that the random variables $V a n d W$ are independent. So, their joint density function will be:

$\begin{array}{rcl} f (v, w) & = & f_{V} (v) \cdot f_{W} (w) \\ = & \{\begin{cases} 6 v w^{2} & for 0 \leq v \leq 1, 0 \leq w \leq 1 \\ 0 & Otherwise \end{cases} \end{array}$

Now, using Jacobian method the required distribution function is determined.

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