Using R please 3 set.seed(42) x_values 1 = data.frame runif(15), runif(15), x3 runif(15) 2 3 x1...
Consider the independent random variables X1, X2, and X3 with - E(X1)=1, Var(X1)=4 - E(X2)=2, SD(X2)=3 - E(X3)=−1, SD(X3)=5 (a) Calculate E(5X1+2). (b) Calculate E(3X1−2X2+X3). (c) Calculate Var(5X1−2X2).
Let 1) a11 x1 + a12 x2 + a13 x3 = b1 2) a21 x1 + a22 x 2+ a23 x3 = b2 3) a31 x1 + a32 x 2+ a33 x 3 = b3 SHOW that if det(A) does not equal 0, where det (A) is the determinant of the coefficient matrix, then x2= det(A2)/det(A) where det (A2) is the determinant obtained by replacing the second column of det (A) by (b1, b2, b3) to the power T.
= = 3, Cov(X1, X2) = 2, Cov(X2, X3) = -2, Let Var(X1) = Var(X3) = 2, Var(X2) Cov(X1, X3) = -1. i) Suppose Y1 = X1 - X2. Find Var(Y1). ii) Suppose Y2 = X1 – 2X2 – X3. Find Var(Y2) and Cov(Yı, Y2). Assuming that (X1, X2, X3) are multivariate normal, with mean 0 and covariances as specified above, find the joint density function fxı,Y,(y1, y2). iii) Suppose Y3 = X1 + X2 + X3. Compute the covariance...
1. Consider a set of vectors S = {X1, X2, X3 } in which X1 = (1,0,0), X2 = (a, 1, -a), X3 = (1, 2, 3a +1) Determine the value (or values) of a for which the set Sabove is linearly independent (LI). 2. Consider a set of vectors T = {y1, y2.ya} in which yı = (1,2,0), y2 = (1, m,5), and y3 = (0,4, n) Determine a condition on m and n such that the set T...
Description for Question 7. A multinomial distribution for three nonnegative counts X1, X2, X3 has joint pdf given by 23 P(X1 = X1, X2 = 22, X3 = x3) (21.3.2.) pi? pºp3", X1 X2 X3 where pi + P2 + P3 1. For genotypes AA, Aa, and aa, the Hardy-Weinberg model puts the respective genotype proportions in the population at (1 - 0)?, 20(1 – 0), and 02, where 0 is the gene frequency of gene type "a" (0 <...
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3, Cov(X1, X2) = 2, Cov(X2, X3) = -2, 5. Let Var(x1) = Var(X3) = 2, Var(X2) Cov(X1, X3) = -1. i) Suppose Y1 = X1 - X2. Find Var(Y1). ii) Suppose Y2 = X1 – 2X2 – X3. Find Var(Y2) and Cov(Y1, Y2). Assuming that (X1, X2, X3) are multivariate normal, with mean 0 and covariances as specified above, find the joint density function fyy, y,(91, y2). iii) Suppose Y3 =...
3) Let (x, y), (X2, y2), and (X3. Y3) be three points in R2 with X1 < x2 < X3. Suppose that y = ax + by + c is a parabola passing through the three points (x1, yı), (x2, y), and (x3, Y3). We have that a, b, and c must satisfy i = ax + bx + C V2 = ax + bx2 + c y3 = ax} + bx3 + c Let D = x X2 1....
Consider the following linear program: Maximize Z-3xI+2x2-X3 Subject to:X1+X2+2 X3s 10 2x1-X2+X3 s20 3 X1+X2s15 X1, X2, X320 (a) Convert the above constraints to equalities. (2 marks) (b) Set up the initial simplex tableau and solve. (9 marks)
Consider the following linear program: Maximize Z-3xI+2x2-X3 Subject to:X1+X2+2 X3s 10 2x1-X2+X3 s20 3 X1+X2s15 X1, X2, X320 (a) Convert the above constraints to equalities. (2 marks) (b) Set up the initial simplex tableau and solve. (9 marks)
2. The random variables X1, X2 and X3 are independent, with Xi N(0,1), X2 N(1,4) and X3 ~ N(-1.2). Consider the random column vector X-Xi, X2,X3]T. (a) Write X in the form where Z is a vector of iid standard normal random variables, μ is a 3x vector, and B is a 3 × 3 matrix. (b) What is the covariance matrix of X? (c) Determine the expectation of Yi = Xi + X3. (d) Determine the distribution of Y2...
4. Testing for significance Aa Aa Consider a multiple regression model of the dependent variable y on independent variables x1, x2, X3, and x4: Using data with n = 60 observations for each of the variables, a student obtains the following estimated regression equation for the model given: 0.04 + 0.28X1 + 0.84X2-0.06x3 + 0.14x4 y She would like to conduct significance tests for a multiple regression relationship. She uses the F test to determine whether a significant relationship exists...