1. Show that if X' , Y' are the deviations of the random variables X and Y from their respective means, then Dr-1-E - üi) r = -1+E) Deduce that -1srs1.

Q: 2. Let us consider a discrete random variable having the pmf given by, k = 1 Px (k) = {2 k = 2. 0, k…

A: Calculate the moment generating function:

Q: If y1, y2,..., ym be a random sample taken from a normal distribution with parameters x and n× n,…

A: Note: Hi there! Thank you for posting the question. In your question, the parameters of the normal…

Q: If X1, X2, ... , Xn are independent random variables having identical Bernoulli distributions with…

A: Here, Xi’s are independent Bernoulli random variables with parameter theeta. a)

Q: 2. Let X1, X2, X3 be three independent random variables with means ui -5, µ3 tion of Y = X1 - 2X2…

A: Given: There are 3 independent variables with mean and variances given as,…

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: The pdf of a uniform random variable is given by: Ax) = 7aSxs a and r>6

A: Task: From the given information, f(X)=2x, 0≤x≤1 Here, the given density function is continuous…

Q: Suppose that Y ~ Normal(0, 1) and define new random variable X by X=Y². Compute ELYI

A: Given that Y~Normal0,1 Here, E(Y)=0V(Y)=1⇒E(Y2)-EY2=1⇒E(Y2)-0=1⇒E(Y2)=1

Q: If X1 and X2 are independent random variables hav-ing binomial distributions with the respective…

A:

Q: Suppose for a random variable X that E(X) = 5 and Var(X) = 3. What is E((X + 3)2)? %3D

A:

Q: Suppose we observe two independent random samples X1,..., Xn, with each X; ~ N(µ1, 0²) and Y1,...,…

A: We want to find the test statistic and p value

Q: We have the following information about the random variables X and Y: 4 8 11 4 225 , Cou (X, Υ) -…

A: The formula to obtain the variance between the two random variables when they are not independent…

Q: Suppose for a random variable X that E(X) = 5 and Var(X) = 3. What is E((X + 3)²)? Type your answer.…

A: By the properties of random variable, Expectation of constant is a constant. i.e., E(a)=a Variance…

Q: Suppose that we observe m iid Bernoulli(0) random variables, denoted by Y₁,..., Ym. Show that the…

A:

Q: Which of the following is equal to Cov (X+ Y, 2X +Y), where X and Y S ? are random variables on a…

A:

Q: Let X and Y be independent Poisson random variables with parameters 0.25 and 0.35,

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: Two independent random variables, X1 and X2, follow Negative Binomial distributions with parameters…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Suppose X,,X2, . ,X, be iid random samples from Uniform(a, b), where b > a. ... Find the method of…

A: It is given that- X1,X2,....,Xn~Ua, b, b>a So mean and variance are given as, mean = x = a+b2…

Q: Suppose X₁ and X₂ are Find UMVUE for μ independent N(μ, 1) random variables, for an unknown…

A: Given Xi~N(μ,1), i=1,2

Q: Let X1, ..., Xn be iid random variables from Poisson(A). a) Find a sufficient statistic for A. b)…

A: It is an important part of statistics. It is widely used.

Q: 2. Suppose that X is a standard uniform random variable and Y|X = x ~Normal(x,x) for 0 ≤ x ≤ 1. Find…

A: Solution (2) There is two different questions So i am solving first

Q: Let X1, X2,,X, be n independent random variables each with mean 100 and standard deviation 30. Let X…

A: Given that μ=100 and σ=30 E(X)=E∑Xi=nμ=100nσ(X)=σ(∑Xi)=30n

Q: Suppose you have two random variables X,Y ux,Hy,o o3,0xY where Cov(X, Y) = 0x.Y You sample both…

A: The provided information is: n=81x¯=50y¯=55σ2x=25σ2y=144σxy=34.50

Q: if Y1 and Y2 are independent Poisson random variable with parameters λ1 and λ2 re- spectively. Then…

A:

Q: Suppose that the random variables Y1, . , Yn satisfy Y, = B ; + e, i= 1,..., n, where #1, ..., In…

A: From the given information, Y1, Y2,....,Yn satisfy Yi=βxi+εi, i=1,2,....,n. Here, x1,x2,....,xn are…

Q: 2. Suppose that X is a standard uniform random variable and Y|X = x ~Normal(x,x) for 0≤x≤ 1. Find…

A: Given that X follows U(0,1) E(x) =1/2 V(x) =1/12   Y|X=x follows N(x, x) Here, we consider mean…

Q: Suppose X1,X2,...,X, from a real-valued random variable X with unknown mean µ and standard deviation…

A: Suppose X1,X2,X3,.....Xn from a real-valued random variable X with unknown mean µ and standard…

Q: If X1, X2, ... , Xn constitute a random sample from anormal population with μ = 0, show that…

A: It is given that X1, X2, …, Xn is a random sample of the normal population with N(0, σ2). That is,…

Q: Let X, be independent Bernoullli random variables with the probability of success, f(x,e) = e*(1-…

A:

Q: Let X be a geometric random variable with parameter px parameter py 1/2 and let Y be a geometric…

A: Geometric distribution:A random variable x is said to follow a geometric distribution, if the…

Q: Suppose that Y, Y2,.-.,Y, are independent random variables from a gamma distribution of the…

A:

Q: Suppose s random sample X, X2, ..., X, of size n is taken from a population with p.d.f 1 f(x;0) = e…

A: a. From the given information, fx,θ=1θ+1e-xθ+1, 0<x<∞, θ>-1        =1θ+1e-xθ+1,…

Q: Suppose that X1,X2, .., X50 is a random sample from a N(300, 25) distribution. With the test H,: u =…

A: Monte Carlo simulation : Monte Carlo Simulation, commonly known as the Monte Carlo Method or…

Q: Suppose we observe two independent random samples X1,..., Xn, with each X; ~ N(µ1,o²) and Y1,...,Yn,…

A: a) Denote μ1, μ2 are the population means for 1st and 2nd populations, respectively.

Q: Suppose that X is a Normal random variable with E(X) = 1 and Var (X) = 1. Define Y =2X + 1. Find P(0…

A: Consider, EY=E2X+1=2EX+1∵EaX+b=aEX+b=2*1+1=3 VarY=Var2X+1=22*VarX∵VaraX+b=a2*VarX=4*1=4 SDY=VarY=4=2

Q: The Poisson random variable X, has pmf f(2)- A, for z = 0, 1,2,3,.... Which of the following is…

A:

Q: Suppose that W is a discrete random variable which takes on values: 12, 17, 22, 27, 32, 37, 42, 47,…

A:

Q: Show that for a random sample of size 2 from N (0, ơ²) population, E[Xq„] = - o/Vr.

A:

Q: Suppose we observe two independent random samples X1,..., Xn, with each X; ~ N(µ1,o²) and Y1,...,…

A: The given values are x¯=10.1,y¯=7.1,sX2=5.5,sY2=6.4,n1=13,n2=19.

Q: Let X and Y be two independent random variables with PMFS 1 for æ = 1, 2, 3, 4, 5 Px(k) = Py(k) = {…

A: From the given information, X 1 2 3 4 5 P(X) 1/5 1/5 1/5 1/5 1/5 And Y 1 2 3 4 5 P(Y)…

Q: Suppose that the time, in hours, required to repair a heat pump is a random variable X having a…

A:

Q: If continuous random variable normally distributed with mu = 256.43 and J = 27.11 , what is P(225.75…

A:

Q: IfX is a random variable that has a uniform distribution on the interval [o, 10), then PX+ 10 27 is…

A: Continuous uniform distribution: A random variable X is said to have the rectangular distribution or…

Q: Let X,Y, Z be random variables each having a mean µ and variance o². rurther, let Cov(X,Y) = 2,…

A: In question, Given that X, Y, Z are three random variables with mean mu and variance sigma^2. And,…

Q: Suppose a discrete random variable X takes only three values 0, 2 and 3. If P(0)=0.5, P(2)=0.2 and…

A:

Q: Suppose that the number of accidents occuring on a highway each day is a Poisson random variable…

A: Consider X be the random variable representing number of accidents in an highway.    X follows…

Q: Let X and Y be random variables having the same distribution. Show that Cov(X +Y, X – Y) = 0. |

A: Given that  X and Y are same distribution thenE(X2)=E(Y2) , E(X)=E(Y) Show that Cov(X+Y,X-Y)=0

Q: For the random variables X,Y Cov(X,Y) = -0.9 if Z=3-X then what is Cov(Z,Y)=???

A: Given - Cov ( X , Y ) = -0.9 Z = 3-X

Q: .. Let X, Y, Z be random variables each having a mean µ and variance o². rurther, let Cov(X, Y) = 2,…

A: In question, Given that X, Y, Z are three random variables with mean mu and variance sigma^2. And…

Q: Suppose a random variable Y uniformly distributed over the interval [2, 7]. 1. What is f(y)?

A: It is given that Y follows Uniform(a = 2, b = 7) To find : The probability density function of Y.

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.