Let X - Geom(p). Let s 2 0 be an integer. Show that P(X > s) = (1 – p)s. (Hint: The probability that more than s trials are needed to obtain the first success is equal to the probability that the first s trials are all failures.) a. b. Let t 2 0 be an integer. Show that P(X >s + 1 | X > s) = P(X > t). This is the memoryless property .[Hint: P(X > s + t and X > s) = P(X > s + t).] A penny and a nickel are both fair coins. The penny is tossed three times and comes up tails each time. Now both coins will be tossed twice each, so that the penny will be tossed a total of five times and the nickel will be tossed twice. Use the memoryless property to compute the conditional probability that all five tosses of the penny will be tails, given that the first three tosses were tails. Then compute the probability that both tosses of the nickel will be tails. Are both probabilities the same? C.
Let X - Geom(p). Let s 2 0 be an integer. Show that P(X > s) = (1 – p)s. (Hint: The probability that more than s trials are needed to obtain the first success is equal to the probability that the first s trials are all failures.) a. b. Let t 2 0 be an integer. Show that P(X >s + 1 | X > s) = P(X > t). This is the memoryless property .[Hint: P(X > s + t and X > s) = P(X > s + t).] A penny and a nickel are both fair coins. The penny is tossed three times and comes up tails each time. Now both coins will be tossed twice each, so that the penny will be tossed a total of five times and the nickel will be tossed twice. Use the memoryless property to compute the conditional probability that all five tosses of the penny will be tails, given that the first three tosses were tails. Then compute the probability that both tosses of the nickel will be tails. Are both probabilities the same? C.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![Let X - Geom(p). Let s 2 0 be an integer.
Show that P(X > s) = (1 – p)s. (Hint: The probability that more than s trials are needed
to obtain the first success is equal to the probability that the first s trials are all
failures.)
a.
b.
Let t 2 0 be an integer. Show that P(X >s + 1 | X > s) = P(X > t). This is the
memoryless property .[Hint: P(X > s + t and X > s) = P(X > s + t).]
A penny and a nickel are both fair coins. The penny is tossed three times and comes up
tails each time. Now both coins will be tossed twice each, so that the penny will be
tossed a total of five times and the nickel will be tossed twice. Use the memoryless
property to compute the conditional probability that all five tosses of the penny will be
tails, given that the first three tosses were tails. Then compute the probability that both
tosses of the nickel will be tails. Are both probabilities the same?
C.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2499b8bc-1366-4df9-b724-a514eec3636e%2F02f9c3b9-a17b-4108-ba99-21b9305491d4%2Ftuo2sd.png&w=3840&q=75)
Transcribed Image Text:Let X - Geom(p). Let s 2 0 be an integer.
Show that P(X > s) = (1 – p)s. (Hint: The probability that more than s trials are needed
to obtain the first success is equal to the probability that the first s trials are all
failures.)
a.
b.
Let t 2 0 be an integer. Show that P(X >s + 1 | X > s) = P(X > t). This is the
memoryless property .[Hint: P(X > s + t and X > s) = P(X > s + t).]
A penny and a nickel are both fair coins. The penny is tossed three times and comes up
tails each time. Now both coins will be tossed twice each, so that the penny will be
tossed a total of five times and the nickel will be tossed twice. Use the memoryless
property to compute the conditional probability that all five tosses of the penny will be
tails, given that the first three tosses were tails. Then compute the probability that both
tosses of the nickel will be tails. Are both probabilities the same?
C.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 4 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman