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

Q: Let X and Y be two independent N(0,1) random variables and consider Z = 3+ X + YX , Ww = 3 + Y. Then…

A: Result  If X and Y are independent then  E(g(X)h(Y))=E(g(X))E(h(Y)) Cov(X,Y)=0

Q: cores on a 100-point final exam administered to all applied calculus classes at a large university…

A: (a) What percentage of students taking the test had scores between 60 and 80?First, let's calculate…

Q: X and Y are two discrete random variables. If X and Y are negatively correlated, then: ož-y_ož + o3.…

A: It is given that the two discrete random variables are negatively correlated.

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: Let X and Y be two random variables and let r, s, t, and u be real numbers. a. Show that Cov(X+s,…

A: Given: X and Y be two random variables and let r, s, t, and u be real numbers.  We have to show that…

Q: (TRUE / FALSE) For two random variables, X and Y, Var(X+Y) = Var(X)+Var(Y) if X and Y are…

A: Let X is a random variable. Then the variance of X, denoted by Var(X), is a measure of dispersion of…

Q: Let X be a continuous random variable. Prove Var(X) > 0.

A: Solution:- Given that let X be a continuous random and prove that Var(X) > 0.

Q: Let X and Y be random variables with finite variance. Prove that |ρ(X, Y)| = 1 implies that there…

A: Let's assume that |ρ(X, Y)| = 1, which means that the correlation coefficient between X and Y is…

Q: Suppose that X and Y are random variables with E(XY)=E(X)E(Y). The. X and Y (Must be/ cannot be/ may…

A: E(XY)=E(X)E(Y)

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: Show that if X and Y are two discrete random variables (i.e., elementary random variables) then ZX +…

A: The objective of this question is to prove that if X and Y are two discrete random variables, then Z…

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

Q: Let X and Y be two independent N(0,1) random variables and consider Z = 3 +X+ 2XY² , W = 5 + X. Then…

A:

Q: Consider the sample space S= {(-2, 4), (-1, 1), (0, 0), (1, 1), (2, 4)}, where each point is assumed…

A: Given sample space is, S=(-2, 4), (-1, 1), (0, 0), (1, 1), (2, 4). Each point is equally likely.…

Q: 2. Let X and Y be random variables such that V(X) = V(Y). Show that Cov(X + Y, X - Y) = 0.

A: we have given that  V(X)=V(Y) and C(X,Y)=C(Y,X)   ,C(X,X)=V(X) ,  C(Y,Y)=V(Y)

Q: Suppose that the joint CDF of the random variables X and Y is given by 0, x < -2 or y < –5

A: Given that Fx,y=0, x&lt;-2 or y&lt;-538, -2≥x&lt;2, -5≤y&lt;312, x≥2 and -5≤y&lt;312, -2≤x&lt;2 and…

Q: Let X, and X, be independent random variables. Suppose the mean of X, and X2 are 5 and 2; and…

A: Given, Let X1 and X2 are the independent random variables Suppose, the mean,  E(X1)=5  E(X2)=2  The…

Q: Let X1, X2, ..., Xn ~ exp(A) be a random sample. Show that X is sufficient for 1/A.

A: Given:  X1,x2,.....xn from exponential distribution with parameters lambda  Then to show that xbar…

Q: Let X1, X2, .. ,Xn form a random sample from B(1,0). Find minimal sufficient statistics.

A:

Q: Suppose X, Y and Z are three independent N(0, 1) random variables and U = X, V = Y + X and W =…

A: Sol

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

A:

Q: Let X1, X2 and X3 be independent and identically distributed random variables that follow a Poisson…

A: Given:- X1 , X2 , X3 , are independent and identically random variables X1 , X2 , X3  ~ Poisson…

Q: Let X be a random variable such that a. V(3x-3) b. E(3x-3) E(X²) = 58 and V(X) = 40. Compute

A: Answer:- Given, X be a random variable such that  E(X2) = 58 and V(X) = 40               (a) Find…

Q: Is cov(X, Y) random?

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

Q: Let X1 - b(n1, p) and X2 ~ b(n2, p) be independent random variables. a) Find the m.g.f. of Y = X1+…

A: Given that X1 follows b(n1, p) and X2 follows b(n2, p) and they are independent.

Q: Let X be a random variable such that X B( 12,8/9).

A:

Q: Given that X and Y are independent random variables and E(X) = 4, E(Y) - 7, Var(X) = 3. Var(Y) = 6.…

A: given data   E(X) = 4, E(Y) - 7, Var(X) = 3. Var(Y) = 6. find Var(10X - 3Y) = ?

Q: Let Y₁ 1 X=(x,-X₂), where X, and X₂ are independent random variables and each of them is distributed…

A: Given that the independent random variables X1 and X2 follows χ22 distribution.

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: Let X, Y, and Z be jointly distributed random variables. Prove that Cov(X + Y, Z) = Cov(X, Z) +…

A: The covariance between two variables is given as follows (provided the expectation of random…

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

A: Given: There are three vectors.

Q: Suppose that X is a geometric random variable with parameter π. Show that P(X = n+k|X > n) = P(X =…

A:

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

A:

Q: A random variable X is called symmetric if X and -X are identically distributed. Show that X is…

A:

Q: We have two independent random variables X, and X2. Let X,~N(5,15) and X2~x?. Calculate P(X, – 5 >…

A: