Concept explainers
a.
Find the
Check whether the probability changes for three tosses.
Find the probability of getting the first head in four tosses.
Mention the probability distribution of the given random variable r.
a.
Answer to Problem 19CRP
The probability of getting a head in the second trial is 0.25.
Yes, the probability change for three tosses is 0.125.
The probability of getting a head in the fourth toss is 0.0625.
The given random variable follows a geometric distribution with
Explanation of Solution
Geometric distribution:
- There should be n independent trials.
- Each trial has two outcomes.
- The probability of success is the same for each trial.
- The random variable n represents the number of trial in which the first success occurs.
The given random variable is based on getting the first head in tossing a coin and it satisfies the above conditions. Hence, it follows a geometric distribution.
The probability mass
Where,
From the given problem, the probability of getting a head while tossing a coin is 0.5. That is,
Therefore, the probability distribution of the given random variable n is
The probability of getting a head in the second trial is obtained below:
Therefore, the probability of getting a head in the second trial is 0.25.
The probability of getting a head in the third trial is obtained below:
Therefore, the probability of getting a head in the third trial is 0.125.
The probability of getting a head in the fourth trial is obtained below:
Therefore, the probability of getting a head in the fourth trial is 0.0625.
The given random variable follows a geometric distribution with
b.
Find the probability of getting a head in the fourth trail.
Find the probability of getting a head after four trials.
b.
Answer to Problem 19CRP
The probability of getting a head in the fourth trial is 0.0625.
The probability of getting a head after four trials is 0.0625.
Explanation of Solution
Calculation:
The probability of getting a head in the fourth trial is obtained below:
Therefore, the probability of getting a head in the fourth trial is 0.0625.
The probability of getting a head after four trials is obtained below:
Therefore, the probability of getting a head after four trials is 0.0625.
Want to see more full solutions like this?
Chapter 5 Solutions
Understandable Statistics: Concepts and Methods
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
- Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman