Let X, Y & Z be independent uniform random variables on the interval [ 0,1 ] . let W= min {X,Y,Z} What is the expected value of(1- w/a)2

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: 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: Let X and Y be random variables with common range { 1, 2} and such that P(X=1)%3D0.39, P( Y=1)=0.46…

A: In the joint probability distribution row total shows the marginal probability of X and column total…

Q: Consider the bivariate distribution for the random variables x and y. The expected value of a linear…

A: We want to tell you which one is the correct choice.

Q: For a uniform random variable U∼U(0,14)U∼U(0,14), find the probability P(U>11)P(U>11): P(U>11)

A: From the provided information, U~U(0, 14) a = 0 and b = 14

Q: Let X₁, X₂ be a random sample from N (1,1) and Y₁, Y₂ be a random sample from N (0,1), where the…

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Q: Let X(n,p) denote a binomial random variable with parameters n and p. Show that X(n+1,p)>=st X(n,p).

A: Given To prove that

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A: We have given that, X & Y are two random variables which are not independent.  If MX,Y(t1,t2) is…

Q: X and Y are random variables such that Var(X) = 4, Var(Y) = 6 and Var(X+Y) = 16. Calculate Var(a X +…

A: We want to find V(aX+bY)= ?

Q: Two random variables X and Y have joint char- acteristic function yl@,m)=exp(-2@,² – 80;) (i) Show…

A:

Q: Let random variable X be uniform in the interval (0, 1). Define random variable Y = aX + b where a…

A: Given that X ~ U0,1 and Y=aX+b such that a≠0

Q: The 4-dimensional random vector X has PDF fX(x)={1 when 0≤xi≤1, i=1,2,3,4 and 0 otherwise}. Are the…

A: Step 1: Step 2: Step 3: Step 4:

Q: x is a uniform random variable in the interval (x1,x2). Find the expected value of x

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

A: Given that  Y ~ Uniform (1 , 11)

Q: TRUE OR FALSE. a.) Let X (X₁, X2,..., Xn)' be a random vector with joint cumulative distribution…

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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,…

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Q: let X be a random variable and X-B(10, 0.81) find P(x=7)

A:

Q: he random vector x obtained by adding the vectors x1, x2 and x3 end-to-end has a multivariate…

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

A:

Q: Let x1  and x1 be independent standard normal random variables. If Y1= x1 + 2x2 and  Y2 = 2x1 - x2,…

A: We know, any linear combination of normal distribution is a normal distribution. Here, x1 and x2 are…

Q: Let X1 and X2 be discrete random variables with joint probability distribution x1 = 1, 2; x2 = 1, 2,…

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Q: b) Let Z₁ =*#*~N(0,1), and W₁ =~N(0,1), for i=1,2,3,...,10, then: i) State, with parameter(s), the…

A: Given Zi~N(0,1) and Wi~N(0,1)  Result: t~F(a,b) Then  Mean=E(t)=b/(b-2)…

Q: Show that if X and Y are independent Exp(a)-distributed random vari- ables, then X/Y e F(2, 2).

A: The distribution of a continuous random variable can be identified by its pdf because the pdf of…

Q: Let X and Y be independent discrete random variables and suppose that X+Y=2. Show that X and Y are…

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Q: Let X be a binomially distributed random variable B(n, p) with E(X) = 2 and Var(X) = 4/3. Find n.

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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: Let joint Probability distribution function of random variables X and Y be (1/3 if (x, y) = (1, 1)…

A: The joint probability distribution function for X and Y is, P(x,y)=13, if(x,y)=(1,1)13, if…

Q: For a discrete random variable X, find Var(X) if* Var (5 - 2X) = 12 a)2 b)1 c)3 d)6

A: It is given that, Var (5 - 2X) = 12

Q: Let X1 and X2 be continuous random variables with the joint probability - function fx1,x,(x1, x2),…

A: Hello! As you have posted 2 different questions, we are answering the first question (2.2.5). In…

Q: Let JO, J1,..., J4 independent random variables according to the Ber (r₁) law, where i = 0, 1,...,…

A: In this problem, we are given five independent random variables, denoted as J0, J1, J2, J3, and J4.…

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