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

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.4: Discrete Random Variables; Applications To Decision Making
Problem 15E
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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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