A system receives entities according to the followingdensity function:f(x) = 2(x − a) = (b − a), a ≤ x ≤ b, x ≥ 0-and f(x) = 0 otherwise.1. Derive the cumulative distribution function for a=3,b=5;2. Plot the density and cumulative functions for asample from population x: {0,1, 2, 3, 4,5,6,7,8,9,10};3. Derive the equation of the random variate X when arandom uniform number is generated U using InverseMethod. Use EXCEL to check your answers

As per guidelines we will only answer the first three subparts, please repost other subparts for…

Answered: A system receives entities according to…

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 probability density function of X, the lifetime of a certain type of device (measured in months), is given by so if x 5 x2 Find the following: P(X > 9) = The cumulative distribution function of X: if x 5 The probability that at least one out of 5 devices of this type will function for at least 26 months:
7. Assume that X and Y have joint probability density function given by (2x + 3y) if 0< x<1 and 0
Find the cumulative distribution function for Y if its density is f(y) = { 2(1 – 1/y²), 1 1.5).
A speedboat has two engines, A and B. The joint density function of the lifetimes of the two engines, measured in hours, is: f(A, B) = .125 (A + B) %3D defined on the square: 0 < x < 2 and 0< y < 2. Calculate the probability that the speedboat fails during its first 84 minutes of operation, according to: The boat fails upon either engine failing: The boat fails only when both engines have failed:
Suppose that X and Y have a joint probability density function given by Sce-32-5y if r, y 2 0 fx.x(r, y) = otherwise (a) Determine the value of the normalization constant c. (b) Find the marginal probability density function fx and state the name of the distribution of X. (c) Find the conditional probability density function fy|x=z•
d, e, f
Consider a group of people who have received treatment for a disease such as cancer. Let t be the survival time, the number of years a person lives after receiving treatment. The density function giving the distribution of t is p(t) = Ce-Ct for some positive constant C, and the cumulative distribution function is P(t) = , p(x)dx. Think carefully about what the practical meaning of P(t) is, being sure that you can put it into words. a) The survival function, S(t), is the probability that a randomly selected person survives for at least t years. Find a formula for S(t). b) Suppose that a patient has a 80 percent chance of surviving at least 2 years. Find C. c) Using the value of C you found in (b), find the probability that the patient survives up to (that is, less than or equal to) 1 years. d) Using the value of C you found in (b), find the the mean survival time for patients with this survival function, in years.
The cumulative distribution function of the continuous uniform distribution between con- stants a and b is given by F(x) = P(X ≤ x) = x-a - a x b (a) The probability density function is f(x) = F(r). Find the form of f(x). (b) Find the derivative of f(x) for x = [a, b]. Is f(x) decreasing, increasing or flat in this region? (c) Does f(x) have a single maximum in the region [a,b]? If so, what is it, or if not, why not?
Let X be the proportion of new restaurants in a given year that make a profit during their first year of operation, and suppose that the density function for X is ƒ(x) = 20x³(1 − x) Find the expected value and variance for this random variable. E(X) = = Var(X) 0 ≤ x ≤ 1

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

A system receives entities according to the following density function: f(x) = 2(x-a) ÷ (b-a), a ≤ x ≤ b, x ≥ 0 and f(x) = 0 otherwise. 1. Derive the cumulative distribution function for a=3, b=5;