Question: Sometimes the geometric random variable is defined to be the number of trials, X, preceding the first success. Write down the corresponding pdf and derive

Sometimes the geometric random variable is defined to be the number of trials, X, preceding the first success. Write down the corresponding pdf and derive the moment-generating function for X two ways (1) by evaluating E(etX) directly and (2) by using Theorem 3.12.3. 4.4.9. Differentiate Larsen, Richard J.; Marx, Morris L.. Introduction to Mathematical Statistics and Its Applications, An (p. 259). Pearson Education. Kindle Edition

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