Find the mle of B1. 28. AN AMOJNE 2 THIS OF SuPPOJE SHELE INVESTIGATOR HAS DAHA...
20. For X let E(X)-0 and sd(x)-2, and for Y let E(Y)--1 and sd(Y)-4. Find: (a) E(X-Y) and E (X Y). (b) Var(X- Y) and Var(X+ Y) if X and Y are independent. (c) EGX+ 흘 Y) and Var(1X+] Y) İf X and Y are independent. (d) Repeat (b) if, instead of independence, Cov(X, Y)- 1. soY is VarY larger
2. Consider a simple linear regression i ion model for a response variable Y, a single predictor variable ,i1.., n, and having Gaussian (i.e. normally distributed) errors: This model is often called "regression through the origin" since E(X) = 0 if xi = 0 (a) Write down the likelihood function for the parameters β and σ2 (b) Find the MLEs for β and σ2, explicitly showing that they are unique maximizers of the likelihood function Hint: The function g(x)log(x) +1-x...
1. Suppose YPoisson(A) and Y2 ~Poisson(2X) are two independent observations. (a) Derive the MLE of λ based on (Yi,Yo) (b) Show that the estimator λ (Y + Y)/3 is unbiased for λ and compute its variance. (c) With as much rigor as possible, show that if A is large then (A-X)/v is approximately normally distributed. (d) Derive a 95 percent confidence interval for A based on the asymptotic distribution of λ in part (c) (e) Extra Credit Based on part...
2.4 We have defined the simple linear regression model to be y =B1 + B2x+e. Suppose however that we knew, for a fact, that ßı = 0. (a) What does the linear regression model look like, algebraically, if ßı = 0? (b) What does the linear regression model look like, graphically, if ßı = 0? (c) If Bi=0 the least squares "sum of squares" function becomes S(R2) = Gyi - B2x;)?. Using the data, x 1 2 3 4 5...
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Complete parts (a) through (h) for the data below - 2 -2 1 5 2 5 у 1 2 (a) By hand draw a scatter diagram treating x as the explanatory variable and y as the response variable. Choose the correct scatter diagram below. Ов Ос. A AY Complete parts (a) through() for the data below - 1 0 -2 1 (b) Find the equation of the line containing the points (-1) and (1,5), y2x+ (55)...
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0.95 2. 100 points] for 60 students in hy fall 2013 STA 215 sections is: У- 38.831 + 1.399x . Find the residual for a student who scored 80 on exam 1 and 140 on the final exam. The regression line relating y-final exam score lout of 200 points) to x= e xam 1 score [out of A. -60 B. 10.75 C. -154.7 D.-10.75 3.TA True or false: The SSR is calculated as...
A Gaussian random variable X has mean 2 and variance 4 a) Find P(X < 3). (b) Find P(1 < X < 3) (c) Find P({X > 4}|{X > 3}) (d) Let Y = X^2 . Find E[Y].
Find the complement of the following expressions b) (AB+C)0%E 2. Given the Boolean function F -xy + x'y' y'z 1. Implement it with AND, OR, and inverter 2. Implement it with OR and inverter gates, and 3. Implement it with AND and inverter gate 3. Express the following function in sum of minterms and product of maxterms: a) F(A,B,C,D) - B'DA'D BD b) F (AB+C)(B+C'D) 4.Express the complement of the following function in sum of minterms a) F (A,B,C,D)-2 (0,2,6,11,13,14)...
Problem 2 (20 points) Suppose (Y,X) e R × 10, îl has joint density 1/2e-0.5(y+) T (a) Find the marginal density of Y (b) Find the marginal density of X (c) Deduce P10.7 < X 〈 0.81. (d) Are Y and X independent?
Problem 2 (20 points) Suppose (Y,X) e R × 10, îl has joint density 1/2e-0.5(y+) T (a) Find the marginal density of Y (b) Find the marginal density of X (c) Deduce P10.7