Exercise 5.41 Compound distributions. If Y ~ Poisson(A) then E(Y)= \ and Var(Y)d. The Poisson distribution has only a single parameter so we cannot shift and scale the=distribution by different amounts, which limits its usefulness in certain practical applications.This problem can be addressed by allowing the parameter itself to be a random variable.1. Let Y ~ Poisson(X) where X ~ Exponential (0) and 0 > 0 is a fixed scale parameter.Use the laws of total expectation and total variance and the fact that E(X) = 0 andVar(X) = 0² to show that E(Y) = 0 and Var(Y) = 0(1+0).

Answered: Image /qna-images/answer/621458b5-028c-4bce-a313-a501d7215651.jpg

Answered: 1. Let Y Use the laws of total…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

The germination rate of seeds is defined as the proportion of seeds that, when properly planted and watered, sprout and grow. A certain variety of grass seed usually has a germination rate of 0.80, and a company wants to see if spraying the seeds with a chemical that is known to change germination rates in other species will change the germination rate of this grass species. (a) Suppose the company plans to spray a random sample of 400 seeds and conduct a two-sided test of 0: 0.8Hpusing = 0.05. They determine that the power of this test against the alternative 0.75pis 0.69. Interpret the power of this test.(b) Describe two ways the company can increase the power of the test. What is a disadvantage of each of these ways? (c) The company researchers spray 400 seeds with the chemical and 307 of the seeds germinate. This produces a 95% confidence interval for the proportion of seeds that germinate of (0.726, 0.809). Use this confidence interval to determine whether the test described in…
What is Pr(X = n) for a Poisson random variable with parameter l? What is E(X ) in this case?
X is a Poisson random variable with a rate 11 Calculate P(X = 8)?
1a) Derive a maximum-liklihood estimator for the unknown parameter Y 1b) An experienced sales person completes sales following a Poisson distribution, with a mean rate of Y = 1.8 sales/month. A junior sales person completes sales at a mean rate of Y = 0.85 sales per month Find the probability of the joint sales team (experienced and junior) completing exactly 2 sales in any given months, assuming the two sales people act independently of each other. 1c) Find the probability of the joint sales team (experienced and junior) completing more than 2 sales in any given months
The Bahamas is a tropical paradise made up of 700 islands sprinkled over 100,000 square miles of the Atlantic Ocean. According to the figures released by the government of the Bahamas, the mean household income in the Bahamas is $36,807 and the median income is $34,270. A demographer decides to use the lognormal random variable to model this nonsymmetric income distribution. Let Y represent household income, where for a normally distributed X, Y = eX. In addition, suppose the standard deviation of household income is $12,000. Use this information to answer the following questions. a. Compute the mean and the standard deviation of X. b. What proportion of the people in the Bahamas have household income above the mean? c. What proportion of the people in the Bahamas have household income below $16,000? d. Compute the 70th percentile of the income distribution in the Bahamas.
The number of traffic accidents on a section of the M4 freeway during peak flow periods follows a Poisson distribution with a mean of 2 accidents per hour.i. If X is the random variable representing the number of accidents in 1 hour of a peak flow period then state the possible values of X.ii. Determine the probability of 3 or less accidents on this section of the M4 in a randomly selected hour during a peak flow period.iii. Let Y be the variable representing the number of accidents across a 3-hour peak flow period. State the type of distribution Y has and it’s parameter/s. Use these to determine the probability of 5 accidents during a 3-hour peak flow period.
If the number X of particles emitted during a 1-hour period from a radioactive source has a poisson distribution with parameter equal to 4 and that the probability that any emitted is recorded is p=0.9 find the probability distribution of the number Y of the particles recorded in a 1-hour and hence the probability that no particle is recorded

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

SEE MORE TEXTBOOKS

1. Let Y Use the laws of total expectation and total variance and the fact that E(X) = 0 and Var(X) = 0 to show that E(Y) = 0 and Var(Y) = 0(1+0). Poisson(X) where X Exponential(0) and 0 > 0 is a fixed scale parameter.