Concept explainers
Let
Show that
Want to see the full answer?
Check out a sample textbook solutionChapter 3 Solutions
An Introduction to Mathematical Statistics and Its Applications (6th Edition)
- Show that if X, Y are independent random variables, then Cov(X, Y ) = 0.arrow_forwardThe 4-dimensional random vector X has PDF fX(x)={1 when 0≤xi≤1, i=1,2,3,4 and 0 otherwise}. Are the for components of X independent random variables?arrow_forwardLet V=X+Y and U = X - Y are random variables, then the condition which make the covariance C(U,V)=0 isarrow_forward
- 17. Let die die = {(W₁ W₂) : w₁ = 1, 2, 3, 4, 5, 6; w₂= 1,2,3,4,5,6} and consider two random variables X(W₁=W₂) =W₁ + W₂= Y(w₁, W₂) = W₁ - W₂. Compute Cov(X, Y). Are they independent?arrow_forwardLet X ~ Binom(16, 1/4 ) and Y~Geom( 1/2 ) be two independent random variables. Compute(i) Cov(2X, 3Y ),(ii) Cov(X, 4X).arrow_forwardQ2) A continuous random variable has PDF Kx²+2x+1, -25x5 3. Find K, P(x)>0. X, X² and ¹.arrow_forward
- Let X1, X2, X3 be random variables such that Var(X1) = 5, Var(X2) = 4, Var(X3) = 7, cov(X1, X2) = 3, cov(X1, X3) = -2 and X2 and X3 are independent. Find the covariance between Y1 = X1 – 2X2 + 3X3 and Y2 = -2X1 + 3X2 + 4X3. %3Darrow_forwardShow that for two random variables X and Y, 2 2 var(aX+by) =a²o²+b²oy² + 2abCx X Y XY where a and b are real constants.arrow_forwardSuppose X is random variable whose p.d.f. is f2)=(2x-x²), 0, OSxs2 Suppose X is random variable whose p.d.f. is f(x)={4 elsewhere Find the mode , if it exists.arrow_forward
- There are only two states of the world, when a person is well with probability (1-p) and ill with probability p, where (1-p)= 1/3 and p = 2/3. Consider Adam who has utility function U = (Y1, Y2,1 – p,p) = Y,"-P)Y?, where Y; is the income and i =1 is well and i = 2 is ill. When Adam is well, he earns $1000, but when he is ill, he losses $300 in health expenditures and earnings such that Y2 = $700. What is the maximum total premium that Adam is still willing-to-pay? (1-р).arrow_forwardIf X, Y are standardized random variables and r(aX+bY,bX+aY)= 1+2ab a²+b² I Find r(X,Y), coefficient of correlation between X and Y.arrow_forwardLet X and Y be random variables having the same distribution. Show that Cov(X +Y, X – Y) = 0.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage