Suppose that X is a random variable which takes only two values: -2 and +2, and that Y = aX + b where a and b are positive constants. If Y~ Bernoulli(1/2), what is a?

Q: Suppose X is a random variable such that EX = 50 and V arX = 12. Find (a) E(X 2 ) (b) E(3X + 2) (c)…

A: The given X is a random variable with EX=50 and VarX=12.

Q: Suppose X is a discrete random variable with finite first and second moments. Show that E (x…

A: It is given that X is a discrete random variable with finite first and second moment.

Q: ii) Let X be a random variable taking three values: P(X= a₁) = P₁, P(X=a₂) = P2, P(X=a3) = P3, where…

A: Given Information: Let X be a random variable taking three values: PX=a1=p1, PX=a2=p2, PX=a3=p3,…

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: 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: For the random variable X, E(X+1) = 3 , E(X- +X)= 9 then the value of Var(X) is 10 3 0 2 0 50

A: Given, E(X+1)=3 Then E(X)+1=3          E(X) =2 and E(X2+X)=9       E(X2)+E(X)=9       E(X2)+2=9…

Q: 2. Let X1 and X, be independent random variables with mean u and variance o?. Suppose that we have…

A:

Q: Suppose that V and W are random variables with Cov(V, W) = 0. Which of the following must also be…

A: Solution : V and W are random variable  If V and W are independent  so E(VW) = E(V).E(W) Cov(VW) =…

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: Suppose the joint PMF of random variables X and Y is P(X = x, Y = y) =   …

A:

Q: 3. If X and Y are independent uniform (0, 1) random variables, show that 2 for a > 0 (a + 1)(a + 2)…

A: X and Y are independent U(0,1) random variables:Objective: Show that:

Q: Each front tire on a particular type of vehicle is supposed to be filled to a pressure of 24 psi.…

A:

Q: 3. Let the random variable X have the pmf f(x) = = a) E(X) b) E(X²) c) E(3X²2X + 4) (x+1)² for x =…

A: The provided information is as follows:The probability mass function of  is .

Q: There are three random variables X, Y and Z,for which we know the following information E(X)= 6,…

A: Given,V(X)=18  ,  V(Y)=22   ,   V(Z)=4Cov(X,Y)=-12   ,  Cov(X,Z)=5Cov(Y,Z)=8

Q: Suppose that X andY are random variables with E(X) = 2 , E(Y) = 5 and E(X²) = 8, E(Y?) = 30 and…

A: Given that ; E(x) = 2   ;    E(x2 ) = 8  ; E(y) = 5  ;    E(y2 ) = 30 By using these information we…

Q: Let X and Y be independent random variables such that Var[X] = 4.8 and Var[Y ] = 9.7. [a] How can…

A: We have given thatVar[X] = 4.8Var[Y] = 9.7X and Y are independent random variables.That is,…

Q: There are three random variables X, Y and Z, for which we know the following information E(X)= 6,…

A: Given: There are three random variables X, Y and Z. The given values are:…

Q: If X₁, X2, ..., Xn constitute a random sample of size n from an exponential population, show that X…

A: let X1, X2, ......Xn is an independent identically distributed random variable following an…

Q: Two random variables X and Y have the joint characteristic function Pxr (@,, a, ) = exp(-20f -8a})…

A: