es A1, A2,..., An have a common nonzero fr 2, and the correlation between any pair of r d hence prove that -1/(n-1) ≤p≤ 1. Q = o[X² + b (x₁) i=1 estimate of o2, find a and b. Hence show t Q n Σ i=1 2 (X₂ - X)² (1-p)(n-1)'

Let {Xi} from i to n be IID from Bernoulli(p). Find the MQ estimator of p.

3п 4 6п О 3п 8 O П 4. Find Dx in the Riemann Sum k=1 3п [*] 2 f(*)Ax on the interval [0, using 4 intervals.

2) For a random variable X, its kth-order moment is defined as E(X*). Given the p.d.f. fx(x) of X, its Fourier transform Fx(u) = S fx(x)e¬j2muz dx is also called moment generation function. a) Determine an expression of E(X*) in terms of Fx(u). Hint: consider the kth-order derivative of Fx (u) with respect to u and examine its relationship to the definition of E(X*). b) If X is N(0, o²), we know that Fx (u) = exp (-}(2u)°o²). Apply the above idea to determine E(X3) and E(Xª) in terms of ơ².