how to find E(X), E(Y), E(X^2)

Q: A particle moves along the line in a random walk. That is, the particle starts at the origin…

A: It is given that  PXi=1=0.6, PXi=-1=0.4,

Q: Two iid Gaussian random variables X, and X, have mean my and variance . Their sample mean and sample…

A: Given information: Given that X1 and X2 are two iid Gaussian random variables with mean mx and…

Q: the moment generating function of the random variable is always exist

A: The moment generating function of a random variable x, Mx(t) always exists. or not?

Q: Let $X$ and $Y$ be random variables with the space consisting of the four points…

A: Let X and Y be random variable with the space consisting of four points (0,0)(1,1)(1,0)(1,-1). Here,…

Q: In a certain country, the amount of annual rainfall (in tonnes per m) is modelled through a Gamma…

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Q: Let (X,Y) be a bivariate normal random variable. Assume that the covariance between X and Y is 0.…

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

Q: Suppose that X1 and X2 are random variables with zero mean and unit ariance. If the correlation…

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Q: The number of failures of a testing instrument from contamination particles on the product is a…

A: GivenMean of failure per hour is 0.02λ=0.02Let x be the no.of failure per…

Q: value

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Q: Show that the random variable X = Z and Y = 2?. fact that they are statistically dependent. are…

A: Answer: Using the given data,

Q: The number of alpha particles emitted by a lump of uranium in a given minute is modeled by a Poisson…

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Q: The properties of a joint distribution function for two random variables X and Y are given as (1)…

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Q: Define random variables for discrete and continuous variable?

A: A random variable is a variable with an undefined value, or a function that assigns values to each…

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: If X and Y are independent chi-square random variables with respective parameters r and r,, show…

A: Answer:

Q: Let X1, X2, X3 be 3 independent random variables that fit the Poisson distribution with A k…

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Q: ntinuous random variable

A: The PDF of uniform distribution is, fx=1b-a The moment generating function will be determined as,…

Q: Let X and Y denote two discrete random variables taking the values in x and y respectively. The…

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Q: Let X, Y be independent random variables with exponential distribution of parameter θ > 0. Are the…

A: Solution

Q: What is the distribution of the random vector (X1 +2X2, X - X2)?

A: Given that X follows tri-variate Normal distribution.

Q: The range of the random variable X is {30, 1, 2, 3, a} , where a is unknown. If each value is…

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Q: Let X₁ and X₂ be two independent random variables with normal distributions N(1,9) and N(-3,16),…

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Q: If x and y are two independent random variables, show that +y:x-y={:+}-{:*+), where r+y:x-y denotes…

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Q: Suppose Y1,.…,Yn are independent random variables with probability mass function f(y) = p"(1 –…

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Q: Let X be a random variable distributed as a Normal with mean 0 and variance 2 (i.e., X ~ N(0, 2)).…

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Q: The expected value of the transformation is 0 and the variance is 1. So if Z=0.2, when u = 3 and o =…

A: The value of Z is 0.2, mean is 3, and standard deviation is 0.2.

Q: Xí,..., Xn are independent Poisson random variables with mean \, Find UMVUE for 2.

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Q: Let X1, X2, ... be a sequence of IID random variables with uniform distribution on (0,1). Let Y, =…

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Q: Let X be a random variable distributed as a Normal with mean 0 and variance 2 (i.e., X - N(0, 2)).…

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Q: Suppose that X1,X2,...,X200 is a set of independent and identically distributed Gamma random…

A: Given: Where i = 1 to 200

Q: i) Let X,X2, be two identical independent distributed (iid)random variables ,each X- X2 having chi –…

A: Hello! As you have posted 2 different questions, we are answering the first question. In case you…

Q: Let Y~Po(1) be a poisson distributed variable with parameter 2 = 1. Suppose that, designated on Y, X…

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Q: Suppose X1,.. , X, iid Beta(a,ß) 1. Find the LRT “Likelihood ratio test for Ho: a = B = 1 versus…

A: Note: Hi there! Thank you for posting the question. As you have posted multiple questions, as per…

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

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Q: Suppose that three random variables x,„X,„X, fom a random sample from the uniform distribution on…

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Q: 2.Direction: Classify the random variables as DISCRETE OR CONTINUOUS. 1. The number of votes…

A: According our policy we can answer only first three subpart for remaining please repost the…

Q: Suppose the random variable X follows an Inverse Gaussian distribution with parameters u and 8. Use…

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

Q: 5. Show that given random variables X and Y, Cov(X, E(Y | X)) = Cov(X, Y).

A: For the random variable X and Y, we need to show that: Cov[X, E(Y|X)] = Cov(X,Y)

Q: The data of two groups, each group contains two random variables (X1,Y1 and X2,Y2) and each of 30…

A: Given information: The data represents the values of the variables X1, Y1, X2 and Y2.

Q: Y1. Y2. Y, are independent random variables, and .... Y, - Poisson, mean µ,. The fitted values for a…

A: Given the independent random variables Y1, Y2, . . ., Yn and Yi~Poissonμi.

Q: Let X₁, X2,..., Xn be a random sample of size n from Beta (0, 1) 72 Inx, has a chi-square…

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Q: A random variable Y takes values defined by Y = 5x2+19 where X take one of the values {-4, -3, 1, 3,…

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Q: X,X, and X, is a random sample of size 3 from a population *2 with mean value u and variance o?, T,…

A: Answer: For the given data,

Q: Sketch the PDF and CDF of a continuous random variable that is uniform on [0,2]

A: Let X be the continuous random variable uniformly distributed in the interval 0 and 2. Thus, the…

Q: forester randomly locates ten 1-square-yard sampling regions in the area, the probability that none…

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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.

Q: Example: Suppose that X = (X1, X2) has a bivariate Normal distribution with mean (120, 80) and…

A: First, let determine aTX by using aT=1-1 and X=X1X2. aTX=1-1·X1X2=X1-X2 Observing, covariance matrix…

Q: Let x1, x2, .. xn be independent standard normal random variables, where n = 9. What is the…

A: The probability of a random variable X following standard normal distribution lying between 1 and 2…

Q: Let X be a random variable and Y = aX + b with a ̸= 0. Show that the correlation between X and Y is…

A: Given data: Let X be a random variable and Y = aX + b with a ≠ 0. To show: Show that the correlation…