Homework Help is Here – Start Your Trial Now!
Math
Probability
Shashank performs an experiment comprising a series of independent trials. On each trial, he simultaneously flips a set of Z fair coins. Given t hat Sh

Shashank performs an experiment comprising a series of independent trials. On each trial, he simultaneously flips a set of Z fair coins. Given t hat Sh

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 29E
See similar textbooks
icon
Related questions
Topic Video
Question
the accident. Question 16 Shashank performs an experiment comprising a series of independent trials. On each trial, he simultaneously flips a set of Z fair coins. a. Given that Shashank has just had a trial with Z tails, what is the probability that next two trials will also have this result? b. Whenever all the Z coins land on the same side in any given trial, Shashank calls the trial a success. i. Find the PMF for K, the number of trials up to, but not including the second success. Find the expectation and variance of M, the number of tails that occur before the first success where Z = 3 in this case. ii. (Hint: Write M = X, + X2 + .…+ Xy Where X; is number of tails in that occur on unsuccessful trail i and N is number of unsuccessful trails and find E (M) in terms of E (X) and E(N) and for var(M) first write in terms of M | N (i.e. M given N) and later write var(M) in terms of E(N), E (X), var(N), var(X) using the above derived variance equation in terms of M | N.) You are expected to write all the steps involved in deriving E (M), var(M) as mentioned in the hint. ... c. Sandeep conducts an experiment like Shashank's, except that he uses M coins for the first trial, and then he obeys the following rule: Whenever all the coins land on the same side in a trial, Sandeep permanently removes one coin from the experiment and continues with the trials. He follows this rule until the (M- 1)h time he removes a coin, at which point the experiment ceases. Find E[X], where X is the number of trials in Sandeep's experiment. hp
Transcribed Image Text:the accident. Question 16 Shashank performs an experiment comprising a series of independent trials. On each trial, he simultaneously flips a set of Z fair coins. a. Given that Shashank has just had a trial with Z tails, what is the probability that next two trials will also have this result? b. Whenever all the Z coins land on the same side in any given trial, Shashank calls the trial a success. i. Find the PMF for K, the number of trials up to, but not including the second success. Find the expectation and variance of M, the number of tails that occur before the first success where Z = 3 in this case. ii. (Hint: Write M = X, + X2 + .…+ Xy Where X; is number of tails in that occur on unsuccessful trail i and N is number of unsuccessful trails and find E (M) in terms of E (X) and E(N) and for var(M) first write in terms of M | N (i.e. M given N) and later write var(M) in terms of E(N), E (X), var(N), var(X) using the above derived variance equation in terms of M | N.) You are expected to write all the steps involved in deriving E (M), var(M) as mentioned in the hint. ... c. Sandeep conducts an experiment like Shashank's, except that he uses M coins for the first trial, and then he obeys the following rule: Whenever all the coins land on the same side in a trial, Sandeep permanently removes one coin from the experiment and continues with the trials. He follows this rule until the (M- 1)h time he removes a coin, at which point the experiment ceases. Find E[X], where X is the number of trials in Sandeep's experiment. hp
Expert Solution
steps

Step by step

Solved in 3 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Optimization
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
SEE MORE TEXTBOOKS