q1: Train a variational autoencoder on any image dataset, then use the decoder to generate fake images. Discuss your results after running the model.

q2: (1, 2, 3)

1. Let X1, X2, .., X_be a random sample from a Poisson distribution with parameter ). The mean and variance of a Poisson random variable are 2. If we want to estimate 0 = 24, what is the MLE of 0 . Show the derivation. Poisson Distribution Formula P(X = x)= x! where X = 0, 1, 2, 3, ... 1 = mean number of occurrences in the interval e = Euler's constant ~ 2.71828 2. Let X1, X2, .., Xn be a random sample from the normal distribution, N(H,62). a. If u = 1, What is the MLE of oz b. If u is unknown, what is the MLE of o 3. Derive a closed form solution for the optimal values of w that minimize the loss function L(w) in terms of the n x d matrix X whose i-th row is x and the n x 1 vector y whose i-th entry is yi, (You may assume that any relevant matrix is invertible.) L(w) = > (yi - x] w)2 1=1