4. Suppose X is a random variable such that E( 3X - 7) = 8 and E() 19. What is Var( 70 – 2X ) ?

Q: If the random variable X follows N (0, 2) and Y = 3X, find the mean and vari- %3D ance of Y.

A:

Q: 2. Let X be a random variable. Is it possible that px,x² = 1 for some X? What about PX,x² = -1?

A: Solution

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

A: ANSWER:-

Q: 2. Suppose that X is a random variable with E(X) = 6 and Var(X) = 4. Find the following: a) Е(4X +…

A:

Q: 1) If Var(X-Y) = 2, Var(X+Y) = 4, E(X) = 3 and E(Y) = 1, than what is E(XY)? 2) If X and Y are…

A: Solution is given below

Q: Suppose that Y ~ Normal(0, 1) and define new random variable X by X=Y². Compute ELYI

A: Given that Y~Normal0,1 Here, E(Y)=0V(Y)=1⇒E(Y2)-EY2=1⇒E(Y2)-0=1⇒E(Y2)=1

Q: 4. X and Y are two random variables with variances ožand of respectively and r is the coefficient of…

A: Introduction :  Definition : correlation coefficient: Let X and Y are two quantitative variables.…

Q: 2. Let X be a random variable with E[X] = 15 and Var[X] = 10. Suppose Y = 2X – 7, Use the properties…

A: Given,E(X)=15Var(X)=10and Y=2X-7

Q: Suppose that Z is a discrete random variable with Var(Z) = 1/2 and E(Z) = 2. Match up the following…

A: 1] Var(Z)=12 2] E(Z)=2

Q: Suppose for this random variable X we want to compute P(X ≤ 3)

A:

Q: If X1 and X2 are independent random variables hav-ing binomial distributions with the respective…

A:

Q: Suppose the manufacturer of an item wants to test Ho p= 0.8 against H1 p= 05 for a binomial random…

A:

Q: Suppose for a random variable X that E(X) = 5 and Var(X) = 3. What is E((X + 3)2)? %3D

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Q: We have the following information about the random variables X and Y: 4 8 11 4 225 , Cou (X, Υ) -…

A: The formula to obtain the variance between the two random variables when they are not independent…

Q: Suppose that one variable, x, is chosen randomly and uniformly from [0, 5], and another variable, y,…

A:

Q: Suppose that X and Y are random variables. If we know that V(X)=11 and Y=2X−4, determine σ(Y).

A: Given : V(X)=11 and Y=2X−4 V(Y) = V(2X−4) = 22V(X) = 4*11 = 44

Q: (2) Z is the present value random variable for a pure endowment of 1000 payable at the end of 20…

A: Pure endowment contracts: A pure endowment contract provides the sum assured at the end of the fixed…

Q: Suppose for a random variable X that E(X) = 5 and Var(X) = 3. What is E((X + 3)²)? Type your answer.…

A: By the properties of random variable, Expectation of constant is a constant. i.e., E(a)=a Variance…

Q: Suppose we have two random variables X and Y. For a, b > 0, a2+b2=13. Var(aX) = 16 Var(bY) = 36…

A: Suppose we have two random variables X and Y. For a, b > 0, a2+b2=13. Here we use the…

Q: Suppose that the hazard rate of a certain continuous positive random variable is given by 4t+4. Find…

A:

Q: The amount of detergent in a box of a particular detergent has a uniform distribution with c=24 and…

A: The uniform distribution (continuous) is one of the simplest probability distributions in…

Q: Suppose you have two random variables X,Y ux,Hy,o o3,0xY where Cov(X, Y) = 0x.Y You sample both…

A: The provided information is: n=81x¯=50y¯=55σ2x=25σ2y=144σxy=34.50

Q: 1. Show that if X' , Y' are the deviations of the random variables X and Y from their respective…

A: Given that, Xi' and Yi'are the deviations of random variables X and Y form their means. Xi' = Xi-X¯…

Q: X is an exponential random variable with the population's mean (ux) = 52. %3D What is P(X < 48)?

A: Given data: The given value of the mean is μx=52. The expression for the probability when X&lt;48…

Q: If X1 and X2 are independent random variables hav-ing the geometric distribution with the parameter…

A:

Q: Suppose X, Y and Z are independent random variables with var (X) = 4 , var (Y) = 4 , var (Z) = 1/n…

A: Solution

Q: what is E[XY]?

A:

Q: 5. Suppose that the probability of a defect in a foot of magnetic tape is 0.002. Use the Poisson…

A: As per our guidelines we are supposed to answer only one question per post so i am solving first…

Q: 7. A discrete random variable X taking non-negative integer values has probability gen- erating…

A:

Q: Suppose X1, X2, X3 and X4 are independent random variables, which have the same Bernoulli…

A: Given that  X1, X2, X3, X4 ~ Bernoulli ( p = 1/3 ) X1, X2, X3, X4 are independent  Compute Cov(X1 +…

Q: Since the continuous random variable X is normally distributed with parameters X~N(-3, 9) what is…

A:

Q: Suppose that X is a random variable for which E(X) = μ and Var(X) = σ2. Show that E[X(X − 1)] = μ(μ…

A:

Q: If the time taken to repair a personal computer is a random variable X whose p.d. f is given by · ,0…

A:

Q: Suppose Xis a random variable with E(X) = 2, and E(X2) = 5. Compute the following quantities: a)…

A: Given X is a random variable with E(X) = 2, and E(X2) = 5

Q: Suppose a discrete random variable X takes only three values 0, 2 and 3. If P(0)30.5, P(2)=0.2 and…

A: The discrete random variable X takes only three values 0, 2, and 3. The probabilities are P0=0.5,…

Q: Find the first two moments about the mean for the random variable X defined by X =-2 with prob. 1/3…

A:

Q: Suppose that the time, in hours, required to repair a heat pump is a random variable X having a…

A:

Q: IfX is a random variable that has a uniform distribution on the interval [o, 10], then pfx+ 10 27 is…

A: Let X be a random variable which has a uniform distribution on the interval [0,10], then the pdf of…

Q: Suppose a discrete random variable X takes only three values 0, 2 and 3. If P(0)=0.5, P(2)=0.2 and…

A:

Q: If X1, X2, and X3 constitute a random sample of sizen = 3 from a Bernoulli population, show that Y…

A: X1,X2,X3 are same from a Bernoulli distribution. Y=X1+2X2+X3 Let X1,X2,X3 are from Bernoullip.

Q: , If continuous random variable X is normally distributed with u = 5625 and o = 875.5, what is…

A: Given that X follows a normal distribution with mean= 5625 and standard deviation= 875.5

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

A:

Q: The random variable V has a PMF of PV(v) of c(1/2)n when n = 0, 1, 2, 3 and it is 0 otherwise. Set…

A: The function is PMF if ∑Pi=1 so it follows: c120+c121+c122+c123=1c1+12+14+18=1c158=1c=815 Hence the…

Q: 4.Suppose that X is a random variable for which E(X)=µ and Var(X)=o². Show that E(X(X-1)]=µ(µ-1)+o?

A: It is given that E(X) = μ and Var(X) = σ2

Q: Given that X~N(39,32) A Random variable X is normally distributed and has a mean of 9 C Random…

A: Given that X~N39, 32: X~Nμ, σ2 Here, mean μ=39 and variance σ2 = 9 X~N39, 32 states that X is a…

Q: For the random variables X,Y Cov(X,Y) = -0.9 if Z=3-X then what is Cov(Z,Y)=???

A: Given - Cov ( X , Y ) = -0.9 Z = 3-X

Q: 9.1.1. X, and X, are iid random variables with variance Var[X]. (a) What is E[X, - X2]? (b) What is…

A:

Q: Consider the random variable X such that E(X) = 3 and Var(X) = 2 if the random variable Z = 1+5X.…

A: Given information:Given that the mean and variance of the variable X is 3 and 2.That is, E(X) = 3…

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: The mean of the random variable X is ux = 38 and the coefficient of variation is Vx=0.37. Let Z be…

A: Z = x - μσ