Using 2 independent DRVS X and Y with probability distribution px(x) and py (y) below, find E(Z) where Z = X + Y X 1 2 3 4 Px(x) 1/8 3/16 3/8 3/16 1/8 Y 2 3 4 5 Pr(y) 1/4 1/4 1/4 1/4

Q: Find marginal distributions P(x) and P(y)

A: The objective is to construct the marginal distribution of P(x) &P(y) Given that the joint…

Q: 2) Let the joint probability function of X & Y be defined by Pxx (x, y) = x= 1,2 y = 1,2,3 Find…

A: The joint probability mass function of x and y is, P(x,y)=x+y21;x=1,2 and y=1,2,3 x=1, y=1…

Q: If a probability generating function of a random variable x is Px(s)=(1/3+2/3s)^6 determine…

A: Given: The probability generating function of a random variable X is given as:…

Q: Y = 0 1 2 X = 0 .10 .25 .25 1.05 a .25 p(v) p(x) Find: (a) a. (b) The marginal probabilities for X…

A: Solution: We need to find the value of constant a and the marginal probabilities for X and Y

Q: If 'X' is a continuous random variable, then the expected value is given by O a. SXP(X) O b. No…

A: The symbol used to denote the expected value of a particular random variable is E(X). It is defined…

Q: (1) Let X and Y be independent random variables with distributions tilli 0 1 2 0 1 2 3 Pr(X = r)…

A: Note: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts…

Q: Let X be a discrete random variable having the Poisson distribution with parameter u. we know that…

A: Let X be a discrete random variable having a Poisson distribution with parameter .We know that .

Q: 1. (a) A continuous random variable X has a p. d. f. f(x) = 3x?, 0 a) and (ii)P(X > b) = 0.5. (b)…

A: 1). a). Given P.D.F is: fx=3x2 : 0≤x≤1 i). For PX≤a=PX>a…

Q: For the given probability distribution, X f(x,y) 1 2 5 0.25 0.2 y 10 0.2 0.15 15 0.15 0.05 Determine…

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Q: The random variables X,Y have variance Var(X)=36 and Var(Y)=1 and their correlation is Cor(X,Y)=−34.…

A: Formula used Var ( X+Y) = Var(X)+Var(Y)+2Cov(X,Y)

Q: Let X be a discrete random variable having the Poisson distribution with parameter μ. we know that…

A: Let X be a discrete random variable having a Poisson distribution with parameter μ.We know that…

Q: II. Let X be a discrete random variable with possible values xi, i=1,2,..., and p(xi)=P(X=xi) is…

A: The given statements can be completed as follows, Let X be a discrete random variable with possible…

Q: Consider the three functions I. f(x)= {1-x if 0 < x < 2 {0 otherwise II. f(x)= {1+x if 0 < x < 2 {0…

A: f(x) can be probability distribution function if integration|xf(x)dx = 1 It means the total…

Q: Let X and Y be random variables with Var(X)=0.64, Var(Y)=0.81, and Cov(X,Y) = 0.5. Find each of the…

A: Part (a) Coefficient of correlation ρ(X,Y)The coefficient of correlation ρ  is defined…

Q: 1) Find the Mean and Variance for the following function [1 -x, 0sxs1 1 (10 – x), 1sxs 10 45 f(x) =…

A:

Q: The diameter of a round rock in a bucket, can be messured in mm and considered a random variable X…

A: We want find  Mean= E(x) , variance = var(x)

Q: 7) For the continuous probability distribution f(x) = kx³e-* Where x 20, find mean.

A:

Q: 5. and Y is The joint probability distribution function of two discrete random variable |x -y| 15…

A:

Q: What is the variance of X

A: here given continuous probability density function  c(1- x2)           -1 ≤x ≤ 10…

Q: a. What is the probability that the demand for gasoline in a given week is more than 500 gallons? b.…

A:

Q: Suppose that the random change in value of a financial asset is X over the first day and Y over the…

A: The variance of X+Y is calculated asVarX+Y=VarX+VarY-2CovX,Y

Q: Let X and Y be random variables with Var(X)=0.64, Var(Y)=0.81, and Cov(X,Y) = 0.5. Find each of the…

A: Step 1: a) It is given that, Var(X) = 0.64, Var(Y) = 0.81 and Cov(X,Y) = 0.5. The coefficient of…

Q: If Y is a standard Cauchy random variable, show that Y and are identically distributed. Y

A: Solution

Q: 2. Let X be a random variable with pdf fx(x), and Y = X². %3D (a) Find fx(x|X > 0) (b) Find fy(y|X >…

A: We have to answer questions based on conditional pdf of distribution

Q: Let Y be a continuous random variable with f(y) = {1123 0, Find the mean (µ) and variance (0²) of Y.…

A: Method: integration of continuous distribution.The pdf of continuous random variable  is:

Q: Suppose that the conditional distribution of Y given X = x is Poisson with mean E(Y|x) = x, and that…

A: d) From the given information, The conditional distribution of Y given X=x is Poisson distribution…

Q: Let a continuous random variable X follows normal distribution N(4.0, 16). Find (i) Pr(X 4.6).

A:

Q: Suppose X₁ and X₂ have the following joint distribution X₁ 1 d 2 1/3 1/12 1/6 0 2 1/36 0 0 0 X₂ 1 0…

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Q: Assume that a joint probability distribution function is given by: p(x,y) X 0 5 10 Find: •E(x), E…

A: The joint probability distribution function is given by, P(x,y) y 0 5 10 15 x 0 0 0.1 0 0.1…

Q: The correlation between X and Y Select one or more: a. is the covariance squared b. cannot be…

A: option (d)  Correlation :can be calculated by dividing the covariance between X and Y by the product…

Q: Let Xand Y be two continuous random variables with joint probability density 3x function given by:…

A: The given value are EX=34, EX2=35, EY=38, EY2=15 and EXY=310.

Q: Obtain regression curve of Y on X for the following distribution : y f (x, y) = +1 exp (l + x) y 1+x…

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Q: find the value K and F(x).

A:

Q: The probability density function of a discrete random variable X is given by the following table:…

A: