Let X and Y be random variables having the same distribution. 1 If X and Y are independent, show that Var(X) = E[(X – Y)²]. - 2

Q: A continuous random variable X has the p.d.f. f(x) = (a) Find the mean of X. (b) Find the variance…

A: The probability density function of Xf(x)=1/2e-|x|    for  0                        otherwiseWe have…

Q: Determine the value of c such that f(x) = (c / x2) for x > 1 represents the p.d.f. of a random…

A: Given that  f(x)=c/x2   , x>1

Q: Let u(X) be a nonnegative function of a random variable X. It can be shown that  P(u(X) >= c) = a)…

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

Q: Suppose that 40% of fruit flies possess a certain gene.  We will randomly select fruit flies until…

A: Given that 40% of fruit flies of fruit flies posses a certain gene. So, probability that a fruit fly…

Q: Let X be a Geometric random variable with parameter p = 1/4. Find E(4X + 1)² and V(3 + 2X). Two fair…

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Q: A bucket has three marbles.  Two are black and one is white.  You keep drawing until you get a while…

A: Given information A bucket has 3 marbles 2 Black, 1 white X denotes the total number of marbles…

Q: (a) f(x) = c(x² + 6), for x = 0, 1, 2, 3 5 3 - (:) ( 2² X (b) f(x) = c 3-x for x = 0, 1, 2

A: It is given that a probability distribution of the discrete random variable X.

Q: C2. Let X be a random variable. (a) Let YaX be another random variable. What is EY, in terms of μ =…

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Q: Let X denote the number of VCRs sold during a random week by a certain store. The probability…

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Q: Let X and Y be random variables with Var(X)=0.64, Var(Y)=0.81, and Cov(X,Y) = 0.5. Find each of the…

A: Part (a) Coefficient of correlation ρ(X,Y)The coefficient of correlation ρ  is defined…

Q: C2. Let X be a random variable. (a) Let YaX be another random variable. What is EY, in terms of μ =…

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Q: A grade in a probability course depends on exam scores X1 and X2. The professor, a fan of…

A: As per guidelines of Bartleby,we are giving here solution of first 3 parts only.

Q: Let X be a random variable. (a) Let YaX be another random variable. What is EY, in terms of μ = EX?…

A: Given : X be the random variable  Y=aX

Q: Fact: If X is a compound random variable with X = ₁X₁, ther E(X) = E(X₁) E(N) a. when X are all…

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Q: i. Show that f(x, a, ß) is a distribution ii. Find E(X)

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Q: Let X be a Poisson random variable with E(X) = 3. Find P(2 < x < 4).

A: When X~ Pois(λ) P(X=x)=e-λ λx/x!  ; X=0,1,2,3,.. result: r!=r(r-1)(r-2)..3x2x1

Q: Let X be a discrete random variable with P(X = -1) = .3, P(X = 1) = .45, P(X = 2) = .15 and P(X = 6)…

A: The following information has been given: We have given that X is a discrete random variable.  P(X =…

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

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