C2. Let X be a random variable. (a) Let YaX be another random variable. What is EY, in terms of μ = EX? (b) Using part (a), show that Var (aX) = a² Var(X). (c) Prove that Var(X + b) = Var(X).

Q: Suppose X is a random variable, whose pdf is defined as follows: 2x = (²x) (u(x) - u(x − 3)) where…

A: The solution is given below.Explanation:Given:Given the probability density function (pdf) for a…

Q: 1 The discrete random variable X has Var (X) = 5 Find Var (4X – 3)

A: Given Data: Var(X)=5 Equation: Var(4X-3) ......(1) Simplify the equation (1). Var4X-3=42VarX=16VarX

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: For two random variables X and Y where X∼ exponential(0.5) and Y|X = x ∼ N(5,x2), find E(E(X|Y ))

A: Given, Two random variables X and Y such that X~Exp(0.5) and Y|X=x ~N(5,x2)

Q: The lung cancer hazard rate λ(t) of a t-year-old male smoker is such that λ(t) = 0.027 +…

A: Given that the lung cancer hazard rate  of a t-year-old male smoker as

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: Let rt be a log return. Suppose that r0, r1, . . . are i.i.d. N(0, 0.01^2). (a) What is the…

A: we have given - rt be a log return. Suppose that r0, r1 . . . are i.i.d. N(0, 0.0001). a) since ,…

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: The CDF F(x) of a random variable X is given by; F(x) = { 0, if x 3 } i) the mean and variance of…

A: Here,fx=dfxdx=dcx-14dx=4cx-13                                    ;1<x≤3   Now, find c using the…

Q: Let X be a non-negative random variable that is not a constant. The product E(1/X) times E(X) is…

A: The question is asking whether the product of the expected value of a non-negative random variable X…

Q: Let X be a random variable with discrete pdf f(x) = x/8 if x = 1, 2, 5, and zero otherwise. Find:…

A:

Q: Let Y be a continuous random variable with f(y) = {1123 0, Find the mean (µ) and variance (0²) of Y.…

A: Method: integration of continuous distribution.The pdf of continuous random variable  is:

Q: F(x,y) = { (x+y)/42 ; x = 1,2,3  y = 1,2                 0; elsewhere ] (i) Find the mean for the…

A: F(x,y) : { (x+y)/42 ; x=1,2,3 y=1,2  ; 0 elsewhere } Mean : E(X) = sum(x*P(x))

Q: 3. Let X be a continuous random variable on the interval [0, 1] having cdf Fx(x) = 3x² − 2x³. Let W…

A:

Q: Consider a random variable X having pdf Give the cdf of Y = |X|. ƒx(x) = ² I(-2, 1) (x). 3

A: Given a random variable X having pdf:

Q: Let X and Y be random variables having the same distribution. 1 If X and Y are independent, show…

A: Given that  Let X and Y be random variables having the same distribution.If X and Y are independent,…

Q: Let the joint pdf of random variables X,Y be fx,y (x, y) = a(x + y)e-2-Y, for all æ > 0, y 2 0. Find…

A:

Q: Q1 Let X be a non-negative discrete random variable. Prove that the expected value of X satisfies…

A:

Q: Calculate the Average and the variance

A:

Q: Find the value of Var(X − 2Y + 7).

A: It is given that Var(X)=6, Var(Y)=3  and ρ(X, Y)=-14.

Q: If the odds against R occurring are 1:7, then find P(R) and P(R'). P(R)= (Simplify your answer.)…

A: For the defined event R, the odds using the ratio against R occurring is given as: No. of…