Example 4.2. Suppose the joint distribution of X and Y is given by1P(X = x,Y = y) = (x + y³) I{1,4}(x)I{-1,0,1,3} (3):Find the distribution of1. Z = X +Y2. W = min(X,Y)3. V 3 XҮ

From the given information, PX=x,Y=y=142x+y2, I1,4xI-1,0,1,3y Consider, the two way table, Y|X 1…

Answered: Example 4.2. Suppose the joint…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Let X1, . . . , Xn i.i.d. U([θ1, θ2]), i.e., X1, . . . , Xn are independent and follow a uniform distribution on the interval [θ1, θ2] for θ1, θ2 ∈ R and θ1 < θ2. Find an estimator for θ1 and θ2 using the method of moments.
The U.S. divorce rate has been reported as 3.6 divorces per 1000 population. Assuming that this rate applies to a small community of just 500 people and is Poisson distributed, and that x = the number of divorces in this community during the coming year, determine the following: a. E(x) b. P(x=1) c. P(x= 4) d. P(x6) e. P(2x5)
LetX1,X2,...,Xn be a sequence of independent and identically distributed random variables having the Exponential(λ) distribution,λ >0, fXi(x) ={λe−λx, x >0 0, otherwise Define the random variable Y=X1+X2+···+Xn. Find E(Y),Var(Y)and the moment generating function ofY.
If X has the discrete uniform distribution f(x) = 1k for x = 1, 2, ... , k, show that(a) its mean is μ = k + 12 ;(b) its variance is σ2 = k2 − 112
Let X1,X2,... be a sequence of identically distributed random variables with E|X1|<∞ and let Yn = n−1max1≤i≤n|Xi|. Show that limnE(Yn) = 0
The US divorce rate has been reported as 3.6 divorces per 1000 population. Assuming that this rate applies to a small community of just 500 people and it’s Poisson distributed, and that x = the number of divorces in this community during the coming year, determine the following : a. E(x) b. P(x=1) c. P(x=4) d. P(x6) e. P(2x5)
The random variable X has a Bernoulli distribution with parameter p. A random sampleX1, X2, . . . , Xn of size n is taken of X. Show that the sample proportionX1 + X2 + · · · + Xnnis a minimum variance unbiased estimator of p.Given that X1, X2, . . . , Xn forms a random sample of size n from a geometric population withparameter p, show thatY =n∑j=1
13) Random variables X and Y have joint pdf fXY={4xy, 0≤x≤1, 0≤y≤1fXY={4xy, 0≤x≤1, 0≤y≤1 Find Correlation and Covariance
Let X1,...,Xn be a random sample from the distribution f(x) = 2x, 0 < x < 1. Find the distribution of the sample maximum X(n)
The U.S. divorce rate has been reported as 3.6 divorces per 1000 population. Assuming that this rate applies to a small community of just 500 people and is Poisson distributed, and that x = the number of divorces in this community during the coming year, determine the following: d. P(x≤6) e. P(2≤x≤5)
Suppose X1, . . . , Xn are i.i.d. from a continuous distribution with p.d.f. fθ(x)=1/2(1+θx)if −1≤x≤1, where θ ∈ [−1, 1] is an unknown parameter. (a) Find E(X1).(b) Find the MME for θ. (c) Compute the variance of your MME from part (a).

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Example 4.2. Suppose the joint distribution of X and Y is given by 1 P(X = x, Y = y) 42 ; (x + y²) (1,4}(x)1{-1,0,1,3) Find the distribution of 1. Z = X+Y |3D