Question

In: Statistics and Probability

In Example 6.33 we found the distribution of the sum of two i.i.d. exponential variables with...

In Example 6.33 we found the distribution of the sum of two i.i.d. exponential variables with parameter λ. Call the sum X. Let Y be a third independent exponential variable with parameter λ. Use the convolution formula 6.8 to find the sum of three independent exponential random variables by finding the distribution of X + Y.

Expert Solution

Answer:

Given Data

we found the distribution of the sum of two i.i.d. exponential variables with parameter λ.

Let Y be a third independent exponential variable with parameter λ.

x = sum of two expoential distribution.

distribution

and distribution

let pdf of x be f(x)

and pdf of y be g(y)

need to find pdf of z = x + y

so let pdf of z be h(z)

then by convolution formula:

now

, ,

,

so

Hence

,

so distribution

same way it can be proven that distribution

if each distribution.

orchestra answered 1 year ago

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