Let X be an exponential random variable with pdffx(x) = ½³/2, x≥0.Let Y = floor(X), where floor(x) is the largest integer less than or equal to x (i.e. it rounds adown), so floor(0.142) = 0, floor(4.9982) = 4, etc. Note that Y is a discrete random variable,since it can only take the values 0, 1, 2,....(a) Find the pmf py(k) for Y.==(Hint: If you are having trouble, maybe start by calculating py (0) = P(Y = 0), thenPy (1) = P(Y = 1), then generalize.)(b) Let A be the event {Y is even}. Find an expression for the conditional pmf py|A(k).Handy fact: a = when |a| < 1.

Given that X is an exponential random variable with pdf:

Answered: Let X be an exponential random variable…

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

What is Pr(X = n) for a Poisson random variable with parameter l? What is E(X ) in this case?
[Joint PDFS will be covered in Week 7] Let the random variables X and Y be the portions of the time in a day that two alternative routes between Topkapi and Uskudar have congestion (X for Route 1 and Y for Route 2). The joint PDF is given by fxy(x.y) = 2x2 + y? where Osxys1. (b) Assume Z=X+Y and W= XY and traffic experts are interested in the expected values of Z and W. E(Z) = and E(W) =O (Simplify your answers. Do not convert fractions into decimals.) (c) Find the variances of X and Y as well as the covariance between them. v(X) =D VY) =D and Cov(X, Y) =D (Simplify your answers. Do not convert fractions into decimals.) (d) The variance of Z can be found as V(Z) =- (Simplify your answer. Do not convert fractions into decimals.)
Consider a drug that is used to help prevent blood clots in certain patients. In clinical trials, among 5791 patients treated with this drug, 160 developed the adverse reaction of nausea. Use a 0.10 significance level to test the claim that 3% of users develop nausea. Does nausea appear to be a problematic adverse reaction? Identify the null and alternative hypotheses for this test. Choose the correct answer below. A. Ho:p=0.03 H4:p#0.03 O B. Ho: p#0.03 H4:p=0.03 OC. Ho: p=0.03 H4:p0.03 Identify the test statistic for this hypothesis test. The test statistic for this hypothesis test is (Round to two decimal places as needed.) Identify the P-value for this hypothesis test. The P-value for this hypothesis test is (Round to three decimal places as needed.)
Suppose Y is a random variable with E(Y) = 13 and Var(Y) = 6. Solve for the following: (show complete solution) a. E(3Y+ 10) = ? b. E(Y^2) = ? c. Var (10) = ? d. Var (5) = ?
If a discrete random variable X has the following probability distribution: X -2, - 1, 0, 1, 2 P(X) 0.2, 0.3, 0.15, 0.2, 0.15 Use this to find the following: (a) The mean of X and E[X^2]. (b) The probability distribution for Y = 2X^2 + 2 (i.e, all values of Y and P(Y )). (c) Using part (b) (i.e, the probability distribution forY ), find E[Y ]. (d) Using part (a), verify your answer in part (c) for E[Y ]. **Note: Please do not just copy from Chegg!
Suppose X is a random variable such that E(X) = 90 and Var(X) = 7. Compute thefollowing: E(4X + 12) Var(−X) SD(4X)E(X^2) E(X + 3)^2
Suppose the lifespan (in months) of a smartphone battery can be modeled as a continuous random variable with CDF F(x) = 1 − e-x/3 x ≥ 0 What is the probability that the battery lasts between 12 to 15 months?
X is a random variable such that X ~ B(n, p) where mean is 2 and 3 variance is . Find the probability of X is not less than 7. 2
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
Show that the characteristic function of a Gaussian random variable with zero mean and variance o² is (= x (@) = exp -0² w² 2
Let X and Y be random variables having the same distribution. Show that Cov(X +Y, X – Y) = 0.
Let X and Y be independent exponential random variables with parameters 2 and 3. (a) What is the probability that X + Y > 1. (b) Conditional on X + Y = 1, what is the distribution of X.

SEE MORE QUESTIONS

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