since MSE is given by
Where
Prove that MSE(Ô) = Var() + Bias(0)2, i.e., E[(ôn – 0)21 = E[(ên – E(0))21 + [E(Ô) – 012.
Zi= 1 if ith primary unit is in the sample, and Zi=0 otherwise proof: Var (& Zili) = Chint- use EV-VE a partir & Vas 1 & Zit) formula).
Q1 and Q2 (please also show the steps): Q1 Prove that MSE) = Var(ë) + Bias(@?, i.e., El(Ô – 9)2) = E[(O - ECO)?] + [ECO) – 6)2. Q2 Suppose X1, X2, ..., X, are i.i.d. Bernoulli random variables with probability of success p. It is known that = is an unbiased estimator for p. n 1. Find E(2) and show that p2 is a biased estimator for p? (Hint: make use of the distribution of x. and the fact...
Consider the multiple regression model y = X3 + €, with E(€)=0 and var(€)=oʻI. Problem 1 Gauss-Mrkov theorem (revisited). We already know that E = B and var() = '(X'X)". Consider now another unbiased estimator of 3, say b = AY. Since we are assuming that b is unbiased we reach the conclusion that AX = I (why?). The Gauss-Markov theorem claims that var(b) - var() is positive semi-definite which asks that we investigate q' var(b) - var() q. Show...
Below is an atomic instruction: func (var) { var = var + 6; if(var >= 0) { sign = 1; } else { sign = 0; } return sign; } Using func, implement Mutual Exclusion in a multiprocessing system. Also, give the initial value of var and give the entire set of possible initial values for var. Aim to minimize bus traffic.
Using the grammar below: <program> → begin <stmt_list> end <stmt_list> <stmt> | <stmt>; <stmt_list> <stmt> <var> = <expression> <var> → ABC <expression> <var> + <var> | <var> - <var> | <var> 1) show a leftmost derivation and draw a parse tree for each of the statements below: (1) begin A=A-B; B=C; C=A end (2) begin A=B+C; C=C+B end 2) try a rightmost derivation and draw a parse tree for each of the statements in Q1).
Question 1 We prove 0x = 0 as below. Which method of proof did we use? X=X X-x = 0 (1-1)x =0 0x =0 direct proof proof by cases proof by contrapositive Question 2 If direct proof is used to prove the following statement: If x is a real number and x s 3, then 12 - 7x + x*x > 0. What is the hypothesis? 12- 7x+x*x>0 If x is a real number and xs 3 12-7x+x*x<0 If x is not a real number or x > 3 Question 3 If proof by contrapositive is used...
From this density How will get following EX, var(X), M(t). Please proof that in details f(x)= 1 exp(-T) We were unable to transcribe this image
(2. Assume that X, Y, and Z are random variables, with EX) = 2, Var(X) = 4, E(Y) = -1, Var(Y) = 6, E(Z) = 4, Var(Z) = 8,Cov(X,Y) = 1, Cov(X, Z) = -1, Cov(Y,Z) = 0 Find E(3X + 4y - 62) and Var(3x + 4y - 62).
25. (2 points) Below is a proof presented as a proof by contradiction. Restate the proof, using the same ideas, as a proof of the contrapositive of the proposition. Proposition: The sum of a rational number and an irrational number is irrational. Proof: Suppose BWOC that there existr e Q and neR-Q such that run e Q. Sincer is rational, r = for some p, q E Z. Sincer+ne Q, also r+n= for some a, b e Z. Now: r...