21. (15, Assume that a two-dimensional random variable (X,Y) has the followingjoint probability distribution asX-2 04-30.20.10.250.1 0.1a(1) Find the value of a,(2) Find the marginal probability distributions of random variables X and Y,respectively,(3) Find the probability distribution of M = Min(X,Y),(4) Are X and Y independent or not? Why?(5) Calculate the expected value of X, that is E(X).Y

As per our guidelines we can solve first three sub part of question and rest can be reposted.…

Answered: 21. (13; Assume that a two-dimensional…

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 that three random variables X1, X2, X3 form a random sample from the uniform distribution on interval [0, 1]. Determine the value of E[(X1-2X2+X3)2]
4.4. An individual picked at random from a population has a propensity to have accidents that is modelled by a random variable Y having the gamma distribution with shape parameter α and rate parameter β. Given Y = y, the number of accidents that the individual suffers in years 1, 2, . . . , n are independent random variables X1, X2, . . . Xn each having the Poisson distribution with parameter y. (a) Write down a function f so that the joint distribution of Y, X1, . . . , Xn can be described via P(a ≤ Y ≤ b, X1 = k1, X2 = k2 . . . Xn = kn) = Z b a f(y, k1, k2, . . . kn)dy and derive from this expression that, for your choice of f, Y has the Gamma distribution, and that conditionally on Y = y, X1, X2, . . . Xn are independent, each having the Poisson distribution with parameter y. (b) Find the conditional distribution of Y given that X1 = k1, X2 = k2, . . . , kn. (c) An insurance company has observed the number of accidents that an individual has suffered on each of n years and wishes to…
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
A random variable X is uniform from 4 to 8. A Gaussian random variable Y has mean of 10. Approximate the variance ofYY if only 2.5% of its elements is a subset of X.
Suppose two discrete random variables X and Y follows a Binomial distribution. If the random variable X follows Binomial with, X ~ bin (20, 0.25) and the random variable Y follows the Binomial with, Y~ bin(10, 0.35). 2. 3. i. ii. iii. Compute the expected value for X and Y. Compute the variance and the coefficient of variation for X and Y. Suppose further that there exist a random variable W, related to the random variables X and Y by the linear relation, W= 0.4X + 0.6Y and the Covariance( X,Y) is -0.0045, find the expected value of W, (E(W) ) , and the coefficient of variation of W. ( Hint use the transformation properties).
Suppose a random variable Y uniformly distributed over the interval [2, 7]. 1. What is f(y)?
Let x and y be random variable such that the mean and variance of X are 2 and 4. respectively, while the mean and variance of y are 6 and k, respectively. A sample of size 4 is taken from the x-distribution and a sample of size 9 is taken from the y-distribution .If p[(x-y)>8]=0.0228,then what is the value of the constant k?
1(a)Consider the random variable model with density function given byf(x)= { 2kx/45, 0≤x≤5 2k(30−x)/45 , 5≤x≤10 0, otherwise Compute the(i) expected value(ii) standard deviation.comment and discuss on the output of these two components with the type the random variable model defined (b). If f (x)=ce−0.2x , if 0≤x≤10 and 0, otherwiseBased on your computations below, explain and discuss the variousprobabilities with respect to the given exponential function.(i)deduce the constant c, (ii)compute the probabilities(alpha) p(x≥5) (beta) p(x<4) (gamma) p(3≤x≤11)
For an initial investment of 100, an investment yields returns of Xi at the end of period i for i = 1,2, where X1 and X2 are independent normal random variables with mean 60 and variance 25. What is the probability the rate of return of this investment is greater than 10 percent?
A discrete random variable X has the following probability distribution: Value of X 1 2 3 4 5 6 Probability 0.30 0.20 0.15 0.15 0.10 0.10 Find the probability that X is a multiple of 2. ["", "", "", ""] Find the probability X is greater than 1, or P(X > 1). ["", "", "", ""] Find the mean of the random variable X, μX. ["", "", "", ""] Find the variance of the random variable X, σ2XσX2 . ["", "", "", ""] Find the standard deviation of the random variable X, σX.
Let X1,...,Xn be iid random variables with expected value 0, variance 1, and covariance Cov [Xi,Xj] = ρ, for i≠j. Use Theorem of linearity of expectation to find the expected value and variance of the sum Y = X1 +...+Xn.
If Y is a continuous, uniformly distributed random variable over the interval(4,10), then the value of the PDF between 4 and 10 is?

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