please make sure to show all steps and explain them. thanks !

Let /V be a random variable with mean E [M] = m, and Var (N) = v; let A1, A2, ... be a sequence of i.i.d random variables, all independent of NV, with mean 1 and variance 1; let B1, B2, ... be another sequence of i.i.d. random variables, all independent of NV and of A1, A2, ..., also with mean 1 and variance 1. Let A = );_| A; and B = >;_, Bi. 1. Find the following expectations using the law of iterated expectations. Express each answer in terms of m and u, using standard notation. E [AB] = E [NA] = 2. Let N = CI A + c2 be the LLMS estimator of N given A. Find c] and c2 in terms of m and v. 91 =The random variable X is uniformly distributed over the interval [0, 20]. The parameter @ is unknown and is modeled as the value of a continuous random variable O, uniformly distributed between zero and one. 1. Given an observation x of X, find the posterior distribution of O. Express your answers below in terms of 0 and x. Use 'theta" to denote 0 and 'In" to denote the natural logarithm function. For example, In (@) should be entered as 'In(theta)' For 0