13. The joint pmf of two discrete random variables X and Y is given by PX,Y (2, y) = { B₁₂. Px B.x(x+y), x= 1,2,3 and y = 3,4 otherwise 0, (a) What is the value of B? Express your answer as a fraction in lowest terms. (b) Let Z=g(X,Y)= |X-Y. What values does Z take on? (c) Find the pmf pz(z) by constructing a neat, organized table of values. Express your answers as fractions.

Q: 2. Let X and Y be independent random variables with means ux, Hy and variances o, ož. Find an…

A: Solution

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: The profit for a new product is given by Z= 3X- Y- 5. If X and Y are independent random variables…

A: Answer - Given, Z = 3X - Y - 5             X and Y are independent random variables  with σx = 1…

Q: Consider random variables X and Y with x = 0 x = 1 fx,y(x, y) in the table. Find fxy (1|0) and…

A: Let X and Y be represent the random variable having joint probability distribution f(x,y)  We have…

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: 3. Let X1 and X2 be uncorrelated random variables. Let Y₁ = X₁ + X2 and Y2 = X1 - X2. (a) Find…

A: and  are uncorrelated random variables.

Q: 6. Two independent random variables X1=(-1,0,1) and X2=(-1.0) can take the following probability…

A: Expected value is also known as mean or average. It used to take average for discrete or continuous…

Q: Let X be a random variable with E(X)= 1 and E[X(X-1)]=4,then evaluate Var(2-3X).

A:

Q: . Then Var(X+Y+Z) is equal to:

A: Here x , y and z are independent variables  So covariance between them are zero

Q: Q2 Let X₁ and X₂ are two independent chi-square random variables with r₁ and r2 degrees of freedom…

A: Given that  and  are two independent chi-square random variables with  and  degrees of freedom.  and…

Q: If X₁, X₂, X3, .., Xn are random sample from a population with mean μ and variance o², then what is…

A: Given that X1,X2,...,Xn is a random sample from a population with mean μ and variance σ2 and…

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

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: 2 - 4. X, X2, .. is a random sample of N (0,1), find the (X, +X,) Jox,-X2) distribution of Y

A: Solution

Q: 2. (a) Suppose X, Y are independent Geometric(p) random variables. Find Px+y(4). (b) Find Pz(4) if Z…

A:

Q: A9. Let X and Y be independent standard normally distributed N(0, 1) random variables. What is…

A: Given that  X and Y are independent standard normal distribution N(0 , 1).

Q: For any two random variables Y₁ and Y₂, Var(Y₁Y₂|Y₁ = y₁) = y{Var(Y₂|Y₁ = y₁). TRUE

A: Given that Y1 and Y2 are two random variables. Formula: If X is a random variable, then VX=EX2-EX2.…

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: (33) Let X be a random variable with p.d.f. e2k x= 1,2,3 f(x)=- find (1) k (2) E(x+1) O.W

A: Given that X is a random variable with p.d.f f(x)=e2k ; x=1,2,30     ; Otherwise.

Q: Find the covariance between x and y

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

A:

Q: Is cov(X, Y) random?

A: Given :Is cov(X, Y) random?

Q: Show that for two random variables X and Y, 2 2 var(aX+bY) = a¹o²+b²oy² + 2ab Cxx XY where a and b…

A:

Q: If X and Y are independent U (–1, 1) random variables then E (min (X,Y))

A:

Q: We have the following information about the random variables X and Y: |x=2, |y=−1 , ox = 0.25, c X…

A: a)It is given that, .

Q: Let X,Y, and Z be independent exponential random variables with an average of 1. Let W=max(Y,Z) and…

A: Given  X,Y,Z~exp(1)

Q: Two random variables X and Y are defined by X = 0, Y =-1, X² = 2, y² = 4 and Ry -2. Two new random…

A: Given : X¯=0Y¯=-1X2¯=2Y2¯=4RXY=-2W=2X+YU=X-3Y

Q: 2. If X is a random variable taking values 0,1,2,.... and P(X) = ab*, where a and b are positive…

A: i) First part:ii) second part:

Q: 8. IFX is a continuous random variable and y = ax + b then the expected valued of y = ? a. aE(x) b.…

A: y=ax+b

Q: Please explain your answer with steps Suppose X and Y are random variables such that E[X] = -3 and…

A: Suppose X and Y are random variables. Given: E(X) = -3 E(Y) = 6 We have to find E(X-Y). E(X-Y) =…

Q: Z,, Z2, .. is a random sample of N(0,1), find the ution of Y = E,(2, – 2)²

A:

Q: (a) The correlation

A: Answer:

Q: ox²= 3, oy² = 5, oxy = 2, Z=2Y - 4X – 2 a. Determine the variance of Z.

A:

Q: If 'á' is Constant and x be a Random Variable then V(ax)= a? V(x) %3D

A:

Q: X and Y are discrete random variables. If var(X)= var(Y) = o², cov(X,Y)= find var(2X-3Y)

A:

Q: Q2: (b) Let X₁, X2, X3 be uncorrelated random variables, having the same variance o². Consider the…

A: Given that X1,X2,X3 be uncorrelated random variables. That is,…

Q: if x1, X2, ., X, be a random sample from Bin(4,0). ........ is T = x UMVUE ? Justify your answer.

A:

Q: IfXand Y are Two Random Variables and X, Y and o,, are the Corresponding Means and Variance of X and…

A:

Q: Let X and Y be independent random variables distributed as N(-1, 1) and N(1, 1), respectively. .…

A:

Q: Suppose X and Y are independent random variables with X - B (n, p) and Y ~ B (m, p). Show that X +Y…

A: