Let X, Y be independent random variables with exponential distribution of parameter θ > 0. Are the random variables Z = X + Y and W = X / (X+Y) independent?

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

A: Given that X and Y are independent and follows N(0,1)

Q: Derive the variance of the Student's t distribution using the definition Var (X) = ELX²] - Ex)²

A: t distribution: Let us assume X is a random variable following standard normal distribution and Y is…

Q: Let X be a continuous random variable with PDF 2x fx\=) = { otherwise Find the expected value of X.

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Q: Find the mean of the random variable X with PDF S 3x² _if 0 <x < 1, f(x) = otherwise.

A: For the given random variable X, its pdf is

Q: Consider a random variable Y with PDF Pr(Y=k)=pq^(k-1),k=1,2,3,4,5....compute for E(2Y)

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Q: Suppose that f (x) = e* for 0 < x Determine the mean and variance of the random variable.

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Q: f the random variable X follows the uniform distribution U= (0,1) What is the distribution of the…

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Q: Let X1 be a normal random variable with mean 2 and variance 3 and let X2 be a no random variable…

A: Given that X1 follows Normal distribution with E(X1)=2 and V(X1)=3. X2 follows normal distribution…

Q: Let x be a continuous random variable with PDF 3 x > 1 x4 fx (x) otherwise Find the mean and…

A: Given PDF is fX(x) = 3x4,x ≥ 10,otherwise

Q: let x be a random variable with moment generating function Mx(t)=(0.6 + 0.4e^t)^20 then the variance…

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Q: Find the variance of the random variable X with a PDF given by 3x2 S* if - 1< x< 1, f(x) = 2…

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Q: Let x be random variable with E(x) = 2 and var(x) = 3. Verify that random variable x and the random…

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Q: 1) Find the MGF of the random variable X, the pdf is given by ,x E [0,1) ,х€ [1,5) ,otherwise f(x) =…

A: The moment generating function(MGF) for a random variable is given by MXt=EetX where E denotes…

Q: Suppose X and Y are two random variables with covariance Cov(X, Y) = 3 and Var(X) = 16. Find the…

A: The correlation coefficient between two random variables X and Y is defined as:  ρ(X, Y) = Cov(X, Y)…

Q: (Y-1)². Use one decimal place accuracy.

A: Given that  Y ~ Uniform (1 , 11)

Q: A random variable Y has a uniform distribution over the interval (8,, e,). Derive the variance of Y.…

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Q: X and Y be standard normal random variables with correlation ρ. Compute the joint and marginal…

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Q: the maximum likelihood estimator of a random variable x with uniform distribution U(0, 0), 0 =…

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Q: If X, Y are standardized random variables and 1+ 2ab a² + b² find r(X, Y), the coefficient of…

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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: 1.28 On any day, the number of accidents on the highway has a Poisson distribution with parameter A.…

A: We  have to find mean and standard deviation for given uniform distribution...

Q: the random variable Y is such that : E(2Y+3)=6    and    Var(2-3Y)=11 find      E(Y^2)

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Q: A random variable X has only two values a and b with P(X = a) = p , P(X = b) = q (p + q = 1). Find…

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Q: Let X and Y be independent Exp(2) random variables. Define W = X + Y. a) Determine the correlation…

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Q: X and Y be standard normal random variables with correlation p. Compute the joint and marginal…

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Q: Q3/A/ Let X be a r.v with p.d.f f(x) = e-ll - co <x<0, then the value of variance of X is -

A: Given : X is a random variable with PDF             fx=12e-x , -∞&lt;x&lt;∞ To find : Variance of X

Q: calculate the variance of g(X) =X^2+2, where X is the random variable with probability distribution…

A: calculate the variance of g(X) =X^2+2, where X is the random variable with probability distribution…

Q: let X and Y be independent standard normal random variables. Determine the pdf of W = X^2 + Y^2.…

A: Result: If X~N(0,1) then X2~χ2(1) χ2(n1)+χ2(n2)=χ2(n1+n2)  E(χ2(n))=n and V(χ2(n))=2n

Q: Let f(x, y) = x + y for 0 < x < 1 and 0 < y < 1 The Conditional Variance of Y when X = ; is

A: From the given information, the joint density function for X  and Y is,