Consider a decision problem with A= (a1, a2) and e=[0,1]. Define a class of randomized actions A = (aj, aj, aj, a) where a = (p, 1-p), i-1,2,3,4 and P = P(as). Let X1, X2 be a random sample from Bin(1, 0). Define a randomized decision rule 5*(1, 2) defined as aj, (1,2)=(0,0) a (1,2)=(0,1) 8*(1,2)= aj, (1,2) (1,0) a, (1,2)=(1,1) Let T=X+X2. Compute a randomized decision rule 60 as 6(t) E(6*(X1, X2)|T=t)=E(6*(X₁, X₂)). Show that R(0,5) = R(0,5). (14 MARK)
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![Consider a decision problem with A= (a1, a2) and e=[0,1]. Define a class of
randomized actions A = (aj, aj, aj, a) where a = (p, 1-p), i-1,2,3,4 and
P = P(as). Let X1, X2 be a random sample from Bin(1, 0). Define a randomized
decision rule 5*(1, 2) defined as
aj, (1,2)=(0,0)
a (1,2)=(0,1)
8*(1,2)=
aj, (1,2) (1,0)
a, (1,2)=(1,1)
Let T=X+X2. Compute a randomized decision rule 60 as
6(t) E(6*(X1, X2)|T=t)=E(6*(X₁, X₂)).
Show that R(0,5) = R(0,5).
(14 MARK)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F02f04e40-88b2-4c7b-b34f-34913154bebd%2F5ee07692-d72c-4ee7-8782-66fdbb6b5368%2Fycz345_processed.jpeg&w=3840&q=75)
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- Let Y1, Y2, Y3, Y4, and Y, be i.i.d. random variables from a population with mean µ and variance o². Further, let Y = (Y, +Y½ +Y3 +Y4+Y;) denote the average of these five random variables. Now consider a different estimator of µ called W w = }Y + }Y½ + }Y, + }Y, + Y, What is the variance of W? That is, calculate Var|W] Hint: Use the properties of expectations, variances, etc. 187 800 800 187A data processing company has a training program for new salespeople. After completing the training program, each trainee is ranked by his or her instructor. After a year of sales, the same class of trainees is again ranked by a company supervisor according to net value of the contracts they have acquired for the company. The results for a random sample of 11 salespeople trained in the last year follow, where x is rank in training class and y is rank in sales after 1 year. Lower ranks mean higher standing in class and higher net sales. Person 1 2 3 4 5 6 x rank 8 11 2 4 5 3 y rank 7 10 1 3 2 4 Person 7 8 9 10 11 x rank 7 9 10 1 6 y rank 8 11 9 6 5 Using a 1% level of significance, test the claim that the relation between x and y is monotone (either increasing or decreasing). Verify that the Spearman rank correlation coefficient . This implies that the P-value lies between 0.002 and 0.01. State…A data processing company has a training program for new salespeople. After completing the training program, each trainee is ranked by his or her instructor. After a year of sales, the same class of trainees is again ranked by a company supervisor according to net value of the contracts they have acquired for the company. The results for a random sample of 11 salespeople trained in the last year follow, where x is rank in training class and y is rank in sales after 1 year. Lower ranks mean higher standing in class and higher net sales. Person 1 2 3 4 5 6 x rank 2 4 5 3 7 9 y rank 3 6 5 8 9 11 Person 7 8 9 10 11 x rank 10 1 6 8 11 y rank 10 1 4 7 2 Using a 10% level of significance, test the claim that the relation between x and y is monotone (either increasing or decreasing). Estimate the P-value.
- A data processing company has a training program for new salespeople. After completing the training program, each trainee is ranked by his or her instructor. After a year of sales, the same class of trainees is again ranked by a company supervisor according to net value of the contracts they have acquired for the company. The results for a random sample of 11 salespeople trained in the last year follow, where x is rank in training class and y is rank in sales after 1 year. Lower ranks mean higher standing in class and higher net sales. Person 1 2 3 4 5 6 7 8 9 10 11 x rank 3 1 4 10 8 2 9 7 5 6 11 y rank 2 4 3 6 7 1 5 9 10 8 11 Using a 0.05 level of significance, test the claim that the relation between x and y is monotone (either increasing or decreasing). (a) What is the level of significance? (b) Compute the sample test statistic. (Use 3 decimal places.)Consider two independent random variables X and Y with Means of 17 and 21. Assume the variance for the first variable is 1 and that for second variable is 2. Define a new variable as: 3 *X + 4*Y 3*X- 4*Y Calculate the new mean and variance for each case.3. (Competing patterns among coin flips) Suppose that Xn, n 2 1 are i.i.d. random variables with P(X1 = 1) = P(X1 = 0) = }. (These are just i.i.d. fair coin flips.) Let A = (a1, a2, a3) = (0,1, 1), B = (b1, b2, b3) = (0,0, 1). Let TA = min(n 2 3: {X,-2, Xn-1, Xn) = A} be the first time we see the sequence A appear among the X, random variables, and define Tg similarly for B. Find the probability that P(TA < TB). (This is the probability that THH shows up before TTH in a sequence of fair coin flips.)
- An ordinary (fair) coin is tossed 3 times. Outcomes are thus triple of “heads” (h) and tails (t) which we write hth, ttt, etc. For each outcome, let R be the random variable counting the number of tails in each outcome. For example, if the outcome is hht, then R (hht)=1. Suppose that the random variable X is defined in terms of R as follows X=6R-2R^2-1. The values of X are given in the table below. A) Calculate the values of the probability distribution function of X, i.e. the function Px. First, fill in the first row with the values X. Then fill in the appropriate probability in the second row.11. Module 1, Chapter II, Descri X 2 W S uny.edu/d21/le/content/498730/Home?itemidentifier=D2L.LE.Content.ContentObject.ModuleCO-14686306 F2 # 3 80 E D F3 C eText Contents Names James 4 Use the randbetween () function in Excel to Generate ten random grades between 30 and 100 for the following students for a random exam. Find the mean, median, mode (if any), variance, and standard deviation for these data grades. Graph a bar chart representing the grades and the names, explaining the mean and median in the data context. Paul $ Lisa Patrick Juan Tony Jack David Jack Paul 888 FA R F Grades % 5 V 2 X P Section 2.3 Exercises FS T MacBook Air A 6 B F6 Y & 7 H F7 X U N Paraphase - Google Docs X * 8 J ► FB 1 9 M K F9 O 1 0 F10 Untitled document - Goog x L P . 18 + = F12 11 + 门 T ? 2 ⠀ deleteTheorem 3: Let x - (x1,X2 -- . Xp . .., x,) be a data set with a sample mean ĩ and a sample variance S. Also, let y = (y. Y2 ..yp m, Ya) be a data set with a sample mean ỹ and a sample variance S. Finally, let z = x - y such that z- (X1- yı, X2 – y2 -- .X - Ya... . , Xn – Yn). Show that i -i - ỹ.
