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)
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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
Transcribed Image Text:fv (v) = J2v lo 3w² fw (w) = to for 0 ≤v≤1 otherwise for 0≤w<1 otherwise
Expert Solution
Step 1

Given that the random variables V and W are independent. So, their joint density function will be:

fv,w=fVv·fWw=6vw2for 0v1, 0w10Otherwise

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

 

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