The probability density of a random variable is(k> 0,0 < x <∞0).f(x) = ax²e-kxFind (a) the coefficient a, (b) the distribution function of the randomvariable X, (c) the probability that the random variable belongs to the interval(0, 1/k).

Answered: Image /qna-images/answer/ea0aa702-1fd8-49e8-b4a6-3ffb88060be5.jpg

Answered: The probability density of a random…

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

5 Suppose the distribution function of the continuous random variable is (1-e *, -5x x>0; F(x) = 0, x3); (2) the density function f(x)
Let X be a discrete random variable taking values {x1, x2, . . . , xn} with probability {p1, p2, . . . , pn}. The entropyof the random variable is defined asH(X) = −Σpilog (pi) Find the probability mass function for the above discrete random variable that maximizes the entropy.
f(x) = {**/3, Let X be a random variable with density function -1< x < 2, elsewhere. Find the expected value and the covariance of g(X) = 4x + 3.
Two discrete random variables X and Y have joint probability mass function (pmf) (a) (b) (c) ƒ(x) = { 5 0 Calculate the value of k. Show that f(x|y) Show that f(y x) = k n(n+1) = 1 n 1 8 x = 1,2,..., n; y=1,2,...,x. otherwise
3- Remission time for a certain group of leukaemia patients (X, measured in months) Has cdf 0, F(X) = {₁º- e-x/³, x < 0 x ≥ 0 a) Find the pdf b) What is the probability that a random selected patient will be in remission for 2 to 5 month?
7
A continuous random variable X can take only values in the interval [0, 4]. In this interval, the probability that X takes a value greater than x is equal to ax^2 + b. (i) Determine the values of a and b. (ii) Find the cumulative distribution function F(x).
The probability density function of the Pareto distribution is given as: f(x) =- (x>0) (1+x)*1 Show that: Var(x) = ( α- 1), (α-2)
Ch: Estimating Random Variables Q: The beta distribution plays an important role in Bayesian statistics. It has two parameters, called shape parameters. Let X and Y be independent uniform random variables on the interval [0,1]. Estimate via simulation the pdf of the maximum of X and Y and compare it to the pdf of a beta distribution with parameters shape1=2 and shape2=1. Use 'dbeta()'. (use R-code)

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

The probability density of a random variable is (k > 0, 0 < x <∞0). f(x) = ax²e-kx Find (a) the coefficient a, (b) the distribution function of the random variable X, (c) the probability that the random variable belongs to the interval (0, 1/k).