Question

In: Advanced Math

Give the density of an exponential distribution, then derive the moment generating function.

Expert Solution

(a)

Density of an Exponential Distribution is given by:

, (1)

for x 0

= 0 for x < 0

(b)

Step 1:

Moment Generating Function is given by:

(2)

Step 2:

Substituting (1) in (2), we get:

between limits 0 to

Step 3;

Applying limits, we get:

Thus, answer is:

,

Colby Messinger answered 2 years ago

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