There are only two states of the world, when a person is well with probability (1-p) and i with probability p, where (1-p) = 1/3 and p = 2/3. Consider Adam who has utility functio U = (Y,, Y2, 1 – p,p) = Y,ª-P)y?, where Y; is the income and i =1 is well and i = 2 is il || 11 he C1000 b :11 he 1
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- 1. Determine the requested probabilities. -2 -1 1 2 f(x) 0.2 0.4 0.1 0.2 0.1 a) P(xs 2) b) P(x > -2) c) P(-1 sx< 1) d) P(x = 2 or xs-1)Consider two individuals (1 and 2) and assume their preferences over gamblesover [0, infinity) can be represented respectively by U1 (p) = Sigma p (ai) multiply by squareroot of (ai) and U2 (p) = Sigma p (ai) multiply by exponential of (ai), where p(ai) is the probability p assigns to (ai). Are the two individuals risk-averse, risk-loving or risk-neutral? Compute the Arrow-Pratt measure of absolute risk aversion for the twoindividuals? Compute the certainty equilvalent for the two agents for the gamble thatpays 0 with probability 1/2and 3 with probability 1/2What is the expected value of this lottery? What can you say about the comparison betweenthe expected value and the certainty equivalent (this quantity is calledrisk premium)?let X ~ n(8, 1.5) wwhat is the rpobability associated with an outcome between (6.5, 9.5)?
- ) If the probability of a person getting a job is x / 3 The probability of not getting a job is 2/3 . So what is the value of xange of Pla x C ■ Bb Probability que X Bb Statistics and p X X learn-eu-central-1-prod-fleet01-xythos.content.blackboardcdn.com/60d4531e78936/3438094?X-Blackboard-S3-Bucket-learn-eu-central-1-prod-fle... Probability question sheet N Netflix Esc FnLock b) less than three are damaged. a) all 15 will pass b) none will pass and c) at least 12 will pass. A Z -- Q I 0. The probability of passing an exam is 0.7. Out of 15 students, evaluate the probabilities that Type here to search F1 11. Determine the probabilities of having (a) at least 1 girl and (b) at least 1 girl and 1 boy in 23:12 23/04/2023 Alt 11 X 2 S W X AI F2 Vectors.pdf www 3 43 ww A+ F3 E с F4 4 et V 0 - F5 2/4 | % 5 G 0+ F6 B - Y H & 7 N 200% + @ F8 U J 00* 8 Bb Probability que X W F9 M K * F10 61 ( 9 Alt Gr L 6°C O Δ· F12 2 Probability PX + P 117 PrtSc Home [ 6 Ctrl End +11 } J ENG Insert ( # + PgUp K DeleteIf X and Y are independent RVs, each following N (0, 3), what is the probability that the point (X, Y) lies between the lines 3X + 4Y = 5 and 3X + 4Y = 10?
- Which of the following are valid probability spaces on events {a1,a2,a3}. Justify your answer: (a) P(a1)=14, P(a2)=13, P(a3)=12 (b) P(a1)=0, P(a2)=13, P(a3)=23 (c) P(a1)=0, P(a2)=-13, P(a3)=43Consider 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"]Q6. In the following diagram: Họ: µ = 4 ; H1: µ= 1. f(X) Ho Xp Rejection region Non-rejection region Examine the probabilities represented by the regions, a,b and c. Identify the incorrect statement: A. a = Pr(Type I error 'AND’ Not-Type II error). B. a +b = Pr(Type I error). С.с 3D Pr(Туpe Il error). D. a + b + c = Pr(Type I error 'OR’ Type II error) %3D A. A В. В С. С O D. D
- 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)There are 13 questions in this set. As you go through these questions, use relevant information from previous questions. A manufactured good has two inputs, X is the price of input #1. Y is the price of input #2. These prices are in dollars. Below is the bivariate probability distribution of the prices of these inputs. The covariance between X and Y is 0.4. You will need the covariance later in this set so remember to come back to this value and use it! What is the probability that the price of input #1 will be its smallest value (10)? One decimal Version 1 10 11 12 0.1 0.1 Y 0.1 0.2 0.2 0.1 0.1 0.1 1234Two real numbers, x and y, are randomly selected, both from the interval [0, 10]. What is the probability that, at the same time, their sum is less than 7 and the absolute value of their difference is greater than 2?