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Let Ybe an exponentially distributed random variable with mean ß. Define a random variable X in the following way: X= kif k- 1 ≤ Y

Let Ybe an exponentially distributed random variable with mean ß. Define a random variable X in the following way: X= kif k- 1 ≤ Y

A First Course in Probability (10th Edition)
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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Let Ybe an exponentially distributed random variable with mean 3. Define a random variable X in the following way: X= kif k-1 ≤Y<k for k = 1, 2, . . . . a Find P(X= k) for each k = 1, 2,.... b Show that your answer to part (a) can be written as P(X = k) = (e¯¹/³)^−¹ (1 – e¯¹/B), k = 1, 2,... and that X has a geometric distribution with p = (1 − e¯¹/³).
Transcribed Image Text:Let Ybe an exponentially distributed random variable with mean 3. Define a random variable X in the following way: X= kif k-1 ≤Y<k for k = 1, 2, . . . . a Find P(X= k) for each k = 1, 2,.... b Show that your answer to part (a) can be written as P(X = k) = (e¯¹/³)^−¹ (1 – e¯¹/B), k = 1, 2,... and that X has a geometric distribution with p = (1 − e¯¹/³).
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