Please resolve.

Jack and Sam are both taking a statistics class this summer. They decided to study separately for their exam. The probability that Jack will make an "A" in statistics is 0.6, and the probability that Sam will make an"A" is 0.3. Find the probability that exactly one of Jack or Sam will make an "A"in statistics

Bivariate Gaussian distribution Let X, Y be random variables with E[X] = ux, E[Y] = my, Var[X] = ox, Var[Y] = of, Corr(X, Y) = p. We say that X and Y follow the bivariate Gaussian (Normal) distribution, if their joint probability density function is 2 2 -1 T - HX y - HY (x - UX) (y - HY ) f(x, y) = + 2nox oy V1 - p2 XP 2(1 - p? ) -2 p OX OY OX OY where x, y E R. Show that X, Y are uncorrelated if and only if they are independent. Remark: This is an example where independence coincides with uncorrelatedness.Bivariate Gaussian distribution Let X,Y be random magma; with E[X] = m: E[Y| = M1 Var[X] = a}, Var[Y] = a?\" Corr{X, Y) = ,9. \"We say that X and Y follow the laminate Gauss-tan (NOW) distribution. if their joint probability density function is _ 1 1 3,!!1 2 (avw): (xprym} f{m.yJ2ngarmwp{2u_r [( "x ) + 01' 2.9 \"KW ' where 3.3; 6 R. Show that X, Y are uncorrelated if and only if they are independent. Consider the linear model Y = alX1 + a2X2 +b where the vector (X1, X2) has a bivariate Gaussian distribution with means #1, M2, variances of, 02, and correlation coefficient p12. Consider the vector (X1, Y). One can show (via some involved calculus) that (X1, Y) has a bivariate Gaussian distribution. Determine its two means, two variances, covariance, and correlation coefficient. Remark: In lecture we considered precisely this problem but under the as- sumption that X] and X2 are independent.Q2.12 Assume a random vector x = X1 follows a bivariate Gaussian distribution: (x | p, >), where H = is the mean vector and _ = po102 is the covariance matrix. Derive the po102 formula to compute mutual information between 1, and 12, i.e. I((1, 12). Q2.13 Given two multivariate Gaussian distributions: M(x | /1, 21 ) and (X | #2, _2), where #, and #2 are the mean vectors, and E, and 22 are the covariance matrices, derive the formula to compute