3. Poisson process has intensity of a > 0 arrivals/occurrences per hour. Suppose that exactly one arrival/occurrence occurs in the first hour. Let T be the time at which this arrival/occurrence happens, measured in hours (Thus, the possible values of T are real numbers in the interval [0,1]) (a) What is P (0 T< t) forte [0,1]? Note that we are conditioning on exactly one occurrence/arrival during the first hour. Hint: Consider the number of occurrences/arrivals in the interval [0, t] and in the interval (t, 1], and then it becomes similar to Q2 above. (b) What is the cumulative distribution then of T under the same conditions?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 64E
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3. Poisson process has intensity of a > 0 arrivals/occurrences per hour. Suppose that exactly one arrival/occurrence
occurs in the first hour. Let T be the time at which this arrival/occurrence happens, measured in hours (Thus,
the possible values of T are real numbers in the interval [0,1])
(a) What is P (0 T< t) forte [0,1]? Note that we are conditioning on exactly one occurrence/arrival during
the first hour.
Hint: Consider the number of occurrences/arrivals in the interval [0, t] and in the interval (t, 1], and then it
becomes similar to Q2 above.
(b) What is the cumulative distribution then of T under the same conditions?
Transcribed Image Text:3. Poisson process has intensity of a > 0 arrivals/occurrences per hour. Suppose that exactly one arrival/occurrence occurs in the first hour. Let T be the time at which this arrival/occurrence happens, measured in hours (Thus, the possible values of T are real numbers in the interval [0,1]) (a) What is P (0 T< t) forte [0,1]? Note that we are conditioning on exactly one occurrence/arrival during the first hour. Hint: Consider the number of occurrences/arrivals in the interval [0, t] and in the interval (t, 1], and then it becomes similar to Q2 above. (b) What is the cumulative distribution then of T under the same conditions?
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