Two new random variables Y, and Y₂ are formed using the transformation 2 1 [T]-[0.5 0.5] 1 Find the values of (a), (b) [Cy]
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A: *Answer:
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- Consider the following Gauss/Jordan reaction:Which of the following processes (Xt)t is weakly stationary? A: Xt = 1:6 + Xt 1 + V tB: Xt = 0:6 Xt-1 +V tC: Xt = 0:8 Xt-1 + V tD: Xt = 0:8 t + 0:6 V t – 1 The term (t) is always assumed to be white noise with variance oneFind the P - value if the t-stat= -1.8, N=26, df = N-1, alpha = 0.05; and Ho: Mu1= Mu2; Ha : Mu1> Mu2 - 0.08 - 0.05 - 0.04 - 0.025
- Consider the geometric Brownian motion with σ = 1: dS = μSdt + SdX, and consider the function F(S) = A + BSα. Find any necessary conditions on A, B, and α such that the function F(S) follows a stochastic process with no drift.f X1,X2,...,Xn constitute a random sample of size n from a geometric population, show that Y = X1 + X2 + ···+ Xn is a sufficient estimator of the parameter θ.The impulse response of a DT system is h[n] = 3^(n-1)u[n] . Calculate the input x[n] which generates an output y[n] = 2^(n-1)u[n-1] using z-transform method.
- A certain brand of upright freezer is available in three different rated capacities: 16ft3, 18 ft3, and 20 ft3. Let X = the rated capacity of a freezer of this brand sold at acertain store. Suppose that X has pmfx 16 18 20p(x) .2 .5 3a. Compute E(X), E(X2), and V(X).b. If the price of a freezer having capacity X is 70X – 650, what is the expectedprice paid by the next customer to buy a freezer?c. What is the variance of the price paid by the next customer?d. Suppose that although the rated capacity of a freezer is X, the actual capacityis h(X) = X - .008X2. What is the expected actual capacity of the freezer purchasedby the next customSuppose that Xi ∼ Gamma(αi , β) independently for i = 1, . . . , N. The mgf(moment generating function) of Xiis MXi(t) = (1 − (t/β) )−αi . (a)Use the mgf of Xi to derive the mgf of ∑i=1 Xi . Determine the distribution of ∑i=1 Xi based on its mgf.Let X1 ... Xn i.i.d random variables with Xi ~ U(0,1). Find the pdf of Q = X1, X2, ... ,Xn. Note that first that -log(Xi) follows exponential distribuition.