Let Y ~ N(2,5) and Z = 3Y - 4. Give the Distribution of Z. Explain. Do the same for Y ~ U(2,5).
Let Y ~ N(2,5) and Z = 3Y - 4. Give the Distribution of Z. Explain....
Let Z ~ N(0,1) and let Y = Z2. Find the distribution of Y. Hint: Use moment generating function. Let X ~ N(j = 1, 02 = 4). If Y = 0.5*, find E(Y?). Hint: Use moment generating function.
2) Let Yi,., Yn be iid N(a,a2). Let a~ known Find the posterior distribution p(u|3y). This distribution will depend N (8, T2) and trcat o2, 6, and r2 as fixed and on 2, 6, and 2. Calculations are tedious here. Use the hints given in class and follow through
2) Let Yi,., Yn be iid N(a,a2). Let a~ known Find the posterior distribution p(u|3y). This distribution will depend N (8, T2) and trcat o2, 6, and r2 as fixed and...
7.70. Let X,...,x,; Y,., Y,; Z,..,Z, be respective independent random samples from three normal distributions N(u,a+ B, a) N(4-B+y,a), N(= a + y , a'). Find a point estimator for B that is based on X, Y, Z. Is this estimator unique? Why? If a is unknown, explain how to find a confidence interval for B.
7.70. Let X,...,x,; Y,., Y,; Z,..,Z, be respective independent random samples from three normal distributions N(u,a+ B, a) N(4-B+y,a), N(= a + y ,...
2.) Let Z the set of integers and two binary operations on it: Z23(x,y) → xTy = xy + 3x +3y +6 e Z i) Show (Z,L,T)is an integral domain ii) Find the set of units U(Z)
2.) Let Z the set of integers and two binary operations on it: Z23(x,y) → xTy = xy + 3x +3y +6 e Z i) Show (Z,L,T)is an integral domain ii) Find the set of units U(Z)
Suppose X, Y and Z are three different random variables. Let X obey Bernoulli Distribution. The probability distribution function is p(x) = Let Y obeys the standard Normal (Gaussian) distribution, which can be written as Y ∼ N(0, 1). X and Y are independent. Meanwhile, let Z = XY . (a) What is the Expectation (mean value) of X? (b) Are Y and Z independent? (Just clarify, do not need to prove) (c) Show that Z is also a standard...
Let x[n] and y[n] be periodic signals with common period N, and let z[n] = { x[r]y[n – r) r=<N> be their period convolution. Let z[n] = sin(7") and y[n] = { . 0 <n<3 4 <n <7 Asns? be two signals that are periodic with period 8. Find the Fourier series representation for the periodic convolution of these signals.
Let Xn = a sin(bn+Z), where n ∈ Z, a, b ∈ [0, ∞) are constant,
and Z has a continuous uniform distribution on [−π, π] (i.e. Z ∼
U([−π, π])). Show that Xn is stationary. (Hint: sin(x) sin(y) = 1 2
(cos(x − y) − cos(x + y)) may be helpful).
l. Let Xn-a sin(bn+ Z), where n є z, a, b є lo,00) are constant, and Z has a continuous uniform distribution on [-π, π] (i.e. Z ~...
4. Co ider dĀ, where R is the parallelogram enclosed by the lines x-3y=0, x-3y=4, 2x-y=2, Å 2x - y and 2x-y=7. Fill in the boxes: Let u=x-3y, and v= 2x - y. Then in terms of u and v, we can set up the PX - 3 ingen i 19 = 3/d2=SHH dvdu. (You do not actually evaluate the integral.) dvdu van de integral as: JJ 2 actually salane te imeni)
4. Suppose that Z є R2p has a MVN distribution Nop( 12. E.). Partition Z as Z where X є Rp and Y є Rp. Denote the means of X and Y as μι and μy, respectively. Let μΔ-Ha-ty. Suppose that we obtain IID data Z1, ,Zn from the underlying distribution of Z. Let a (0,1) be a constant (a) Describe how to construct a (1-a)-level convex confidence region (CR) for μΔ when y, is known. Explain. (b) Describe how...
4. Let Xn ~ N(1/n, 1). Show that Xn + Z in distribution, where Z is the standard normal.