Concept explainers
The joint pmf of X and Y is
where x and y are nonnegative integers.
(a) Sketch the support of X and Y.
(b) Record the marginal pmfs
(c) Compute Cov(X, Y).
(d) Determine p. the
(e) Find the best-fitting line and draw it on your figure.
Want to see the full answer?
Check out a sample textbook solutionChapter 4 Solutions
Pearson eText for Probability and Statistical Inference -- Instant Access (Pearson+)
- Suppose that Var(X) = 3, Var(Y ) = 4, and Cov(X,Y ) = 1. (a) Find Cov(2X −Y,X + 3Y ). (b) Find ρ(2X −Y,X + 3Y ) (the correlation between 2X −Y and X + 3Y ).arrow_forwardThe joint pmf of X and Y is f(x, y) = 1/6, 0 ≤ x+y ≤ 2, where x and y are nonnegative integers. Compute Cov(X, Y) and determine the correlation coefficient.arrow_forwardWhat is the value of the beta function, B(x, y), where x and y are positive real numbers?arrow_forward
- 9. (25 points) Let X and Y be a random variables of the continuous type having the joint pdf f(x, y) = 8xy, %3D (a) [10 points] Find fa(1) and fy(y). (b) [15 points] Find Cov(X,Y) and correlation coefficient.arrow_forwardTwo real-valued RVs, X and Y, have joint PDF 1 p(x1, x2) = exp 2TV1- 2(1 - r?) where -1arrow_forwardThe cross power spectrum of X(t) and Y(t) is defined as jo - W 0 and K are constants. Find the cross correlation function.arrow_forward(b) Let X₁, X₂, X3 be uncorrelated random variables, having the same variance ². Consider the linear transformations Y₁ = X₁ + X₂, Y₂ = X₁ + X3 and Y3 = X₂ + X3 . Find the correlations of Yi, Y; for i #j. (5 marks)arrow_forwardCompute using Lagrange Inerpolation f(-0.016) for the data (-1.5, - 14.1014), (-0.75, - 0.931596), (0,0), (0.75 , 0.93 1596), (1.5, 14.1014) .a The answer is not included in the options .b 0.02367 .C 0.02362 .d 0.02366 .e 0.02361 .f 0.02365 .g 0.02364 .h 0.02363 .i 0.02369 j 0.02368arrow_forwardLet X and Y be independent and distributed as N(, 1). Is T = X-Y sufficient?arrow_forward• Find the correlation coefficients between: • x(1) = A, cos(wot) and y(1) = A, sin(@,t). • x(1) = A, cos(@1) and y(1) = A, cos(@,t) and w, ± 01.arrow_forwardJ 2arrow_forwardQ2: (b) Let X₁, X2, X3 be uncorrelated random variables, having the same variance o². Consider the linear transformations Y₁ = X₁ + X₂, X2 + X3. Find the correlations of Y₁, Y; i, Y₂ = X₁ + X3 and Y3 for i + j. =arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage