A statistician developed a computer program to generate an Exponential Random variable. Each time the program is run, it generates a random number drawn from an Exponential distribution with parameter 1.7. The generated number, on each run of the program, is independent of how many times the program has been run. It is also independent of the numbers generated on previous runs of the program. (a) Someone runs the program 15 times. You guess that the number generated on the Sth run is greater than 3. What is the probability that you are right? Your answer correct up to four decimal places. (b) Someone runs the program 15 times. They tell you that the number generated on the Sth run is greater than 2. You guess that the number generated on this (5th) run is greater than 3. What is the probability that you are right? Your answer correct up to four decimal places. (c) What is the probability one will need to run the program more than 8 times before seeing a number greater than 3? Your answer correct up to four decimal places. (d) How many times will someone need to run the program until they expect to see a number greater than 3? Your answer correct up to four decimal places. (Non- integer answers are fine, do not round off!) (e) Someone runs the program 8 times. You guess that the maximum number generated during all these runs is greater than 3. What is the probability you are right? Your answer correct up to four decimal places. (f) Someone runs the program 8 times. They tell you that the number generated on the 5th run is less than 4. Then, you guess that the number generated on that (5th) run is greater than 3. What is the probability you are right? Your answer correct up to four decimal places.
A statistician developed a computer program to generate an Exponential Random variable. Each time the program is run, it generates a random number drawn from an Exponential distribution with parameter 1.7. The generated number, on each run of the program, is independent of how many times the program has been run. It is also independent of the numbers generated on previous runs of the program. (a) Someone runs the program 15 times. You guess that the number generated on the Sth run is greater than 3. What is the probability that you are right? Your answer correct up to four decimal places. (b) Someone runs the program 15 times. They tell you that the number generated on the Sth run is greater than 2. You guess that the number generated on this (5th) run is greater than 3. What is the probability that you are right? Your answer correct up to four decimal places. (c) What is the probability one will need to run the program more than 8 times before seeing a number greater than 3? Your answer correct up to four decimal places. (d) How many times will someone need to run the program until they expect to see a number greater than 3? Your answer correct up to four decimal places. (Non- integer answers are fine, do not round off!) (e) Someone runs the program 8 times. You guess that the maximum number generated during all these runs is greater than 3. What is the probability you are right? Your answer correct up to four decimal places. (f) Someone runs the program 8 times. They tell you that the number generated on the 5th run is less than 4. Then, you guess that the number generated on that (5th) run is greater than 3. What is the probability you are right? Your answer correct up to four decimal places.
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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Question
Transcribed Image Text:A statistician developed a computer program to generate an Exponential Random variable. Each time the program is run, it generates a random number drawn from an Exponential
distribution with parameter 1.7.
The generated number, on each run of the program, is independent of how many times the program has been run. It is also independent of the numbers generated on previous runs of the
program.
(a) Someone runs the program 15 times. You guess that the number generated on the 5th run is greater than 3. What is the probability that you are right? Your answer
correct up to four decimal places.
(b) Someone runs the program 15 times. They tell you that the number generated on the 5th run is greater than 2. You guess that the number generated on this (5th) run is greater than 3. What is
the probability that you are right? Your answer
correct up to four decimal places.
(c) What is the probability one will need to run the program more than 8 times before seeing a number greater than 3? Your answer
correct up to four decimal places.
(d) How many times will someone need to run the program until they expect to see a number greater than 3? Your answer
correct up to four decimal places. (Non-
integer answers are fine, do not round off!)
(e) Someone runs the program 8 times. You guess that the maximum number generated during all these runs is greater than 3. What is the probability you are right? Your answer
correct up to four decimal places.
(f) Someone runs the program 8 times. They tell you that the number generated on the 5th run is less than 4. Then, you guess that the number generated on that (5th) run is greater than 3. What is
the probability you are right? Your answer
correct up to four decimal places.
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