Suppose that X and Y are independent random variables with finite variances such that E(X) = E(Y). Show that: E[(X-Y)2] =Var(X) +Var(Y)

Q: Suppose that x,, X, ..., X and Y,, Y,, ..., Y, are independent random samples, with the variables x,…

A: Given  Xi~ N(μ1,σ12) and Yi~N(μ2,σ22 )

Q: and X, be independent normally distributed random variables. X,has a normal distribution with mean 1…

A: Introduction - Z-score  z=x-μσwhere , μ=population mean x=score σ=standard deviation +

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A: Given:  Random variable x and y are independent with means ux, uy  , varience σ2(x) and σ2(y)  E(x)=…

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Q: Suppose you have a population of size N = 500 with elements x1 = ..., x230 ... = x500 = 0. Let…

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Q: Let X and Y be two exponentially distributed and independent random variables with mean a and p.…

A: Introduction :

Q: Let X₁, X2,..., Xn be a random sample from Uniform(a - B, a + B) (a) Compute the method of moments…

A: It is given that X1, X2,...., Xn is a random sample from Uniformα-β, α+β.

Q: The random variables X₁, X2, and X3 are Stochastic Independent with respective means 9, 4, and 16…

A: Consider three random variables X1, X2, X3, where, X1 have mean µ1 and variance σ12, X2 have mean µ2…

Q: If X,, X2,...,X, constitute a random sample of size n from a population with p.d.f. given by .....…

A: Find MLE of θ

Q: Find the characteristic function of a uniformly distributed random variable X in the range [0,1] and…

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Q: 2. Let X1 and X, be independent random variables with mean u and variance o?. Suppose that we have…

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Q: If the probability density of X is given by f(x) =2x−3 for x > 10 elsewherecheck whether its mean…

A: Solution: From the given information, the probability density function of X is

Q: Let px (x) be the pmf of a random variable X. Find the cdf F(z) of X and its graph along with that…

A: a). Find the cdf F(x) of X and sketch the graph: The probability mass function is given below: X…

Q: Suppose that X,, X2, .., Xm and Y,, Y2,..., Y, are independent random samples, with the variables X,…

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Q: Let X ∼ U(a, b). Use the definition of the variance of a continuous random variable (Equation 2.38…

A: The mean of X is given by:

Q: Suppose that X1,..., X, form a random sample from an exponential-distribu- ton for which the value…

A: Mle is that value of parameter which maximize the likelihood.

Q: Let X1, X2, ..., Xn be independent random variables and Y = min{X1, X2,..., Xn}. n Fy(y) = 1 – II (1…

A: Given that X1, X2, . . . , Xn be independent random variables and Y=minX1, X2, . . . , Xn…

Q: Suppose the random variable y is a function of several independent random variables, say…

A: Given that the random variable y is a function of several independent random variables, say…

Q: If X is Poisson random variable with parameter λ, compute E[1/(X + 1)]

A: We have given that If X is Poisson random variable with parameter λ,  we have to compute E[1/(X +…

Q: What value of C minimized B(X – C), where X is a random variable?

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Q: Let X1,X2,...Xn be a random sample from a Poisson population with parameter A. Then. the sample mean…

A: The Pmf of the Poisson distribution is given below: fx=e-λλxx!;x=0,1, 2, ...,n The maximum…

Q: Two random variables X and Y have the joint characteristic function Pxr (@,, a, ) = exp(-20f -8a})…

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Q: Suppose the random variables X,,X2,X; have the population variance/covariance matrix: 1 -2 0 E=-2 0…

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Q: Find the variance by calculating the first two moments of the random variable X = (- 1 / λ) ln…

A: For U~u(0,1) pd.f. of U is f(u)= 1, 0<u<1 To find mean and variance we find p.d.f. of X.

Q: Let X1, X2,..., Xn be independent exponential random variables with mean if. For example, E(X1)=0,…

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Q: what is E[XY]?

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Q: f X1 and X2 are independent exponential random variables with respective parameters λ1 and λ2, find…

A: Given:    X1, X2 are two independent exponential random variables with respective parameters λ1 and…

Q: Suppose x is a normally distributed for continuous random variable with 4-10 and 6. Find value of xo…

A: First converting the variable into standard normal using z =(x-u)/σ where u is mean and σ is…

Q: Let X and Y be two random variables with E (X) = 1, E (Y) = 2, Var (X) = 1, Var (Y) = 2, !! Cov (X,…

A: Given that the mean of aX+bY is 3  So,  E(aX+bY)=3aE(X)+bE(Y)=3a(1)+b(2)=3a+2b=3a=3-2b ..........(Eq…

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A: a) The required value is calculated as follows: fx=ddxFx      =ddxx24     =2x4     =x2…

Q: A chemical supply company currently has in stock 100lb of a certain chemical, which it sells to…

A: We have given that,  X be the random variable having probability mass function (p.m.f),    X   :-…

Q: Let X1, X2, X3 be random variables each having a mean u and variance o'. Further, Cov(X1 X2) 2,…

A: The mean of a constant is equal to the value of the constant and the mean of sum of random variables…

Q: Suppose that a random vector Y' = (Y1, Y2, Y3) has a multi-normal distribution with mean vector u…

A: Additional Property of Multivariate Normal Distribution: If X~Np(μ,∑), and Y =CX , i.e., X is a…

Q: X and Y are independent random variables, each exponentially distributed with a mean of Find P{X >…

A: GivenTwo exponential distributions X, Y with mean 110 I exponential distribution Mean =1λ=110⇒λ=10So…

Q: 2" Find the characteristic function of the Erlang distribution given byf(x) = n - -ax e U(x) and…

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Q: Let X1, X2, ..., Xn be a random sample from the population N(Ha,02) and Y1,Y2,..., Ym a random…

A: Given information: Given that X1, X2, … , Xn be a random sample from the population N(µx, σ2) and…

Q: Suppose X1, X2,..., X10 are independent random variables, Find P(X1+ X2 +...+ X10 < 25), assuming…

A: It is given that X is a random variable. Therefore, Bernoulli distribution is,

Q: 3x (1+х) Q2. If f(x) = ; 0<x <2 denotes the pdf of a continuous random variable, find mean 14 and…

A: Mean = E(X) = ∫xf(x)dx Variance = E(X2) - E(X)2 Where ,   E(X2) = ∫x2f(x) dx

Q: 11. Suppose X and Y are independent continuous random variables uniformly dis- tributed on the…

A: Given information X and Y independent continuous random variables follows uniform distribution  0 ≤…

Q: 2. Prove that if X is a discrete random variable, a and b are constants, and Y = aX + b, then My (t)…

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Q: (a) Let Y be a random variable distributed as X. Determine E(VY) in terms of r.

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at a…

Q: . Let X be a random variable such that E[X] = 0 and P(-3 < X < 2) = 1/2. Find a non-trivial lower…

A: Here, we have,  E[X] = 0 P(-3&lt;X&lt;2) = 1/2  Now, P(-2&lt;X&lt;2) = 1/2 (Since, X cannot be…

Q: Example 10 : If X is a continuous random variable and Y = aX + b, prove that = a E(X) + b and V(Y) =…

A: It is given that Y=aX+b.

Q: Q1. If Var(X)=3, what is Var(2X + 1)? Q2. Compute the variance for a uniform random variable with a…

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Q: If a random variable X has the moment generating function M,(t) = %3D 2-t' determine the variance of…

A: Given,Mx(t)=22-t

Q: 2. Let the random variables Y,, Y2, .., ¥½ be normally distributed with mean 10 and variance 4. Find…

A: Chi-square distribution: Let us assume x1, x2, ... , xn be n independent standard normal variables.…

Q: The conditional expectation of Y given X-x is x 00 The conditional variance of Y given X-x is ²

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.