A sample space has 3 outcomes, {1,2,3}{O1,O2,O3}. Suppose E={1,2}E={O1,O2}, and F={1,3}F={O1,O3}. If Pr[E]=0.58Pr[E]=0.58 and Pr[F]=0.63Pr[F]=0.63, what is Pr[{2,3}]Pr[{O2,O3}]? equation editor lines are ps
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- A company that manufactures a low-calorie dairy drink wants to determine whether there is preference for the new formula (Formula B) over the standard formula (Formula A). Four judges are asked to drink two glasses in random order, one glass containing Formula A and the other containing Formula B. Each judge is asked which glass they prefer. Based on earlier tests, both formulas are equally preferred. Let Y be the number of judges in the current test that prefer the new formula. 1. Which of the following statements is(are) true? (Then, explain why)A. The success in this experiment is observing four judges who prefer the new formula.B. A single trial of the experiment corresponds to four judges.C. Y~Bin(4,0.5)D. All of the above 2. What is the probability that at least three judges prefer the new formula? (Show solution)A. 0.0625B. 0.2500C. 0.3125D. 0.5000A group of researchers wishes to see if the total number of diseases that occurred in six countries are the same. The data are shown in the table. At α = 0.05 is there enough evidence to reject the claim that the number of diseases in the six countries are the same? Philippines - 8,6,7,10,16 India -6,13,16,10,7 Thailand. -5,8,16,22,12 Singapore. -14,12,8,9,15 Korea. -5,4,32,21,17 Japan. -6,18,15,24,16Suppose that X₁, X₂, Xn and Y₁, Y2, . Yn are independent random samples from populations with means ₁ and ₂ and variances of and o2, respectively. Show that X - Y is a consistent estimator of μ₁ - 2.
- Let X1, X2,..., X3 denote a random sample from a population having mean u and variance o?... Which of the estimators have a variance of 7 X1+X2++X, 7 2X1-X6+X4 2 3X1-X3+X4 2 2(X1+X2+.+X¬) 4 7An electronics store has received a shipment of 20 table radios that have connections for an iPod or iPhone. Ten of these have two slots (so they can accommodate both devices), and the other ten have a single slot. Suppose that six of the 20 radios are randomly selected to be stored under a shelf where the radios are displayed, and the remaining ones are placed in a storeroom. Let X = the number among the radios stored under the display shelf that have two slots. (a) What kind of distribution does X have (name and values of all parameters)? O hypergeometric with N = 10, M = 6, and n = 10 O binomial with n = 20, x = 10, and p = 6/20 hypergeometric with N = 20, M = 10, and n = 6 O binomial with n = 10, x = 6, and p = 6/10 (b) Compute P(X= 2), P(X ≤ 2), and P(X ≥ 2). (Round your answers to four decimal places.) P(X = 2) = P(X ≤ 2) = P(X ≥ 2) = (c) Calculate the mean value and standard deviation of X. (Round your standard deviation to two decimal places.) mean value standard deviation…3. An integer is randomly chosen from the set 1, 2,..., 100. If this integer is divisible by 2 we let Y = 0, and if it is not divisible by 2 but is divisible by 3 then Y = 1. We let Y = 2 in all other cases. Find mean and variance of Y.
- Consider the following scenario: • Let P(C) = 0.3• Let P(D) = 0.8• Let P(C|D) = 0.3 A. P(C AND D) = [ Select ] ["0.30", "0.24", "0.26", "0.11"] B. Are C and D Mutually Exclusive? [ Select ] ["No, they are not Mutually Exclusive.", "Yes, they are Mutually Exclusive."] C. Are C and D independent events?[ Select ]["No, they are Dependent.", "Yes, they are Independent."] D. P(C OR D) = [ Select ] ["0.92", "0.86", "0.60", "1.1"] E. P(D|C) = [ Select ]["0.30", "0.95", "0.24", "0.80"]I roll a die with 10 faces numbered 0-9 and obtain a score X. What is E(X)? In order to obtain a random number between 0 and 99 I roll the die twice obtaining scores X and Y, then set Z = 10X + Y (i.e., the first roll determines the "tens", the second roll the "ones"). Is it true to say that E(Z) = 10E(X) + E(Y)?Q1. Given B = {vi = (0, 1, 1, 1), v2 = (2, 1, –1, -1), v3 = (1, 4, –1, 2), v4 = (6, 9, 4, 2)} %3! %3D B' = {wi = (0, 8, 8), w2 = (-7,8, 1), w3 = (-6,9, 1)} -2 1 6 2 1 -3 0 7 1 A = 1 and T : R4 → R3 such that matrix A is the transformation matrix in relation to B and B' basis. a)Verify that set B is a basis of R*and that the set B' is a basis of R³. b)Find [T(v1)]B, [T(v2)]B [T(v3)]B, [T(v4)]B c) find T(v1), T(v2), T(v3), T(v4)
- Nearly 75% of all deaths in the United States are attributed to just 10 causes, with the top four of these accounting for over 50% of all non-accidental deaths as follows: heart disease (23.4%), cancer (22.5%), respiratory disease (5.6%), and stroke (5.1%).t A study of the causes of n = 307 non-accidental deaths at a local hospital gave the following counts. Heart Respiratory Cause Cancer Stroke Other Disease Disease Deaths 81 80 29 13 104 Do the data provide sufficient information to indicate that the number of deaths at this hospital differ significantly from the proportions in the population at large? Test using the p-value approach. (Use a = 0.05.) State the null and alternative hypotheses. HoiP1 = P2 = P3 = P4 = P5 %D %D : At least one p, is different from Hai Ho: At least one p, is different from the specified value. Ha: P1 0.234; p2 = 0.225; p3 = 0.056; P4 = 0.051; P5 = 0.434 Ho: At least one p; is different from Нai P1 3 Р2 -Р3 — Р4 — P5 Hoi P1 H: No value of p, is the same as…A sample space has 3 outcomes, {O1, O2, O3}. Suppose E= {O1, O2}, and F= {O1, O3}. If Pr[E]= 0.67 and Pr[F]= 0.54, what is Pr[{O2, O3}]?
