The probability distribution for the random varaibles X and Y is shown in the table below. Find the covariance of X and Y                                                           x

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: Let X = b(8,) find E(5+6x) and distribution function.

A: 3) From the given information, X≈b(8, 14) E(X)=8*14=2 Consider, E5+6x=5+6E(X)…

Q: Let X ~ N(0, 2) and Y ~ covariances Cov(X,Y) and Cov(Y, X +Y). Exp(A = 3) be two uncorrelated random…

A: At first remind that                                      Independent ⇒UncorrelatedBut, Uncorrelated…

Q: Define gamma distribution with parameters 5 and 7 and obtain its moment generating function. Hence…

A:

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: A poisson random variables has f(x,3)= 3x e-3÷x! ,x= 0,1.......,∞. find the probabilities for X=0 1…

A: Given: Let X be a Poisson random variable. The probability mass function is provided as:…

Q: 4- Suppose that y is N3(4, 41) and let -2 -4 -1 3 -2 -3 A = 4. %3D %3D 1 y Ay, What is the…

A: Given that y~N3μ, 4𝕀 μ=123 and A=2-2-4-1341-2-3

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: Q3// let X and Y have the joint probability distribution function as : . (x, y) (1,1) (1,2) (1,3)…

A: Given that Joint probability distribution function of X and Y (x,y) (1,1) (1,2) (1,3) (2,1) (2,2)…

Q: QUESTION 2 Consider the following information about 3 random variables, X Y and Z. X|Y- Gamma(2Y2,).…

A: Given: X/Y ~ Gamma( 2Y2, Y) Y~ N(2, 5) From given: E(X/Y)=2Y2Y Var(X/Y)=2Y2Y2 We know that for…

Q: 3. Let X be a uniform random variable that takes values -2, -1, 0, 1, 2. Let Y = X²?. Y\X -2 -1 1 2…

A: Since we only answer up to 3 sub-parts, we'll answer the first 3. Please resubmit the question and…

Q: Use the moment generating function you just proved to verify that for a Poisson distribution, E(X) =…

A: The moment-generating function (mgf) of a random variable X is given by                Mx(t)=E(etx)…

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 Y₁, Y₂ follow a Dirichlet distribution with parameters 6, 4, and 3. Find the probability…

A: Let's and follow a Dirichlet distribution with parameters . The properties of the Dirichlet…

Q: The continuous random variable X has the pdf f(x) = { (a) Find the cdf F of X. 0 x -2 if x 1. (b)…

A: Let X be a continuous random variable with the pdf given f(x),f(x)={0if x&lt;1x−2if x≥1To find:a)…

Q: An epidemic process is such that an infected individual is infectious for a time period which is…

A: Here, given that the epidemic process is such that an individual is infectious for a time period…

Q: 3. (15 points) Let X1 and X2be independent exponential random variables: fx, (x1) = e-#1 and fx,(x2)…

A: # Random variable x1 &amp; X2 are independent exponential random variable  with pdf f(x1)=e^-x1…

Q: Find each probability. (a) X ∼ Gaussian (0, 3). Find P[X > 4.5]. (b) Y ∼ Gaussian (50, 10). Find P[X…

A:

Q: The values of x and their probabilities are listed below.  Calculate the intermediate products to…

A: Given that: x P(x) x * p(x) 32 0.07 2.24 34 0.12 4.08 36 0.24 8.64 38 0.25 9.50 40 0.35…

Q: generating function M,(t) = 2 determine the 2-t variance of X.

A:

Q: (a) Are X and Y statistically independent

A:

Q: A random variable X has a normal distribution N(4,9). (1) Find V(X) and E(X²). (2) Let + be the cdf…

A: The normal distribution of the random variable is N(4,9).

Q: r= 1, 2, 3, ... Determine the moment generating function and hence mean and the variance. Assume P +…

A:

Q: Let X~ N(0, 1) and let Y = -X. (a) Show that Y~ N(0, 1) (by showing that Y has cdf Þ). (b) What is…

A: X follows a standard normal distribution.

Q: Let X be a random variable with discrete pdf f(x) = x/8 if x = 1, 2, 5, and zero otherwise. Find:…

A:

Q: Let X be a random variable such that a. V(3x-3) b. E(3x-3) E(X²) = 58 and V(X) = 40. Compute

A: Answer:- Given, X be a random variable such that  E(X2) = 58 and V(X) = 40               (a) Find…

Q: Let X be a discrete random variable with pmf (a) Find the pmf for Y = X². (b) Find the pmf for U = X…

A: The PMF of random variable X is: f(x)=18      x=-214      x=-114      x=014      x=118       x=2  0…

Q: 1. Let f be the probability density function of a continuous random variable X whose range is…

A: Given: fx=x32,    if a≤x≤b0         otherwise

Q: Find the moment generating function of binomial distrbution and hence find its mean and variance.…

A:

Q: Suppose the random variable X follows an Inverse Gaussian distribution with parameters u and 0. Use…

A: From the given information, the random variable X follows an Inverse Gaussian distribution with…

Q: The random variable 'X' has the Poisson distribution Po(m) and P(X=5) = P(X=4) + %3D P(X=3). Find…

A:

Q: Find the covariance between X and Y. Please provide the solution step by step.

A:

Q: When two continuous variables are compared to each other in order to gain a correlation coefficient,…

A: Correlation : Correlation is defined as a relationship between X and Y, Where X is the independent…

Q: Let X and Y be random variables. Suppose Var(X) = 1.6, Var(Y) = 1.5, and Cov(X, Y) = 0.1. Let Z =…

A: Solution: From the given information, Var(X) =1.6, Var(Y) =1.5 and Cov (X, Y) =0.1. Let Z =…

Q: 2) Let the joint probability function of X & Y be defined by Pxy(x, y) = Find E(Y|X = 2). What is…

A: First we will create the joint probability distribution table for every value of x and y using the…

Q: Please explain your answer with steps Suppose X and Y are random variables such that E[X] = -3 and…

A: Suppose X and Y are random variables. Given: E(X) = -3 E(Y) = 6 We have to find E(X-Y). E(X-Y) =…

Q: Let X be a uniform random variable over the interval 1 to 4 and Y is exponential with a mean of 2.…

A: Correlation Coefficient between two Random Variables: If X and Y be two random variables, then the…

Q: A continuous random variable X has a PDF f(x)= 3x²,0 a} and (ii) P{X >b} = 0.05.

A:

Q: Let joint Probability distribution function of random variables X and Y be (1/3 if (x, y) = (1, 1)…

A: The joint probability distribution function for X and Y is, P(x,y)=13, if(x,y)=(1,1)13, if…