Random variable

1 0 3 8 LetA= 0 3 D 10+10 3 D 1 (a) Find the spectral decomposition of A. (b) Find the spectral decomposition of 3'4 = 2:0 3:11.211". Recall the density of a Poi[).) random variable, where )L is the mean parameter, is p(y; A) : 31:!\" . Show that the Poisson model is an exponential family. For a training set (x1, 3'1), . . . , (Kn, ya), what is the maximum likelihood estimator of the Poisson regression model .Yz' | x,- N P0i(h(TXi))a Where h is the response function of the Poisson family? What is the gradient descent update rule for tting the Poisson regression model? Please show your work. 1. Let X and Y be two random variables with E(2X + Y) = 15, E(X + 21) = 18, V(X) = 4, V(Y) = 9, Cov(X, Y) = 4. (a) Find the expectation E(2X - 71); (b) Find Cov(2X + Y,5X- 21). (c) Find the variance Var(4X - 51). (d) By using the Markov's inequality estimate P(X