Consider the following probability density function of a random variable Xf(x)c(x+1)², if −1≤ x ≤ 1,{ox0,otherwise.(a) What is the value of c such that f (x) is a valid probability density function?(b) What is the mean and variance of X?(c) Let Y = X2, what is the mean of Y?=

Answered: Consider the following probability…

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

Suppose the probability function for x is such that p(x=1)=0.3, p(x=2)=0.4 and p(x=3)=0.3. What is the variance of x ?
The probability density function of a discrete random variable X is given by the following table: Px(X = 1) = .05 Px(X = 2) = .10 Px(X = 3) = .12 Px(X = 4) = .30 Px (X = 5) = .30 Px (X = 6) = .1i Px (X = 7) = .01 Px(X = 8) = .01 i) Compute E(X). ii) Compute Var(X). iii) Compute Px(X 3)
If X is normally distributed with mean 0 and variance 1, what is the probability density function of X2 ?
3) Suppose X is a discrete variable that has the following pr function (pdf) f (X) 1. 0.40 0.20 3 0.15 4. 0.25 a) Calculate the cumulative distribution function (the b) Find the expected value, showing your work: E(X) c) Find the variance, showing your work: Var (X)
Let Y be an exponential random variable with (unknown) mean 0.
A random variable X takes value 1 with probability and the value 2 with the remaining probability. What is the variance of X, Var[X]? O 1/3 3/4 2/3 1/2 O 1/4
The random variable X takes value O with probability, and value 1 with the remaining probability. The random variable Y takes value 100 with probability and value 101 with the remaining probability. What is the relation between the variance of X and the variance of Y? Var[X] Var[Y] "
let x be a discrete random variable with probability function p(x)= cx/20 for x = 2,3,4,5,6,8,12 what is the value of c that makes p(x) a valid probability function?
Prob.5 Find the mean, the median, and the mode of the random variable X with the following probability density functions: (a) Gaussian distribution with parameters μ and o². (b) Exponential distribution with parameter 1. (c) Beta distribution with a = 3 and b = 4. (d) Uniform distribution in the interval (a, b).

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

Consider the following probability density function of a random variable X c(x+1)², if−1≤x≤1, f(x) = 0, otherwise. (a) What is the value of c such that f (x) is a valid probability density function? (b) What is the mean and variance of X? (c) Let Y = X2, what is the mean of Y?