Example Suppose A, B, C fail on demand independently with probability 0.1 each T OR AND AND University of Strathclyde Business School T= ^ た = (A.B) What is the probability of the top A B A event T? 01 0.1 0-1 Probability of Top Event Exact P(T) = P(A.B) + P(A.C) − P((A.B).(A.C)) = = P(A.B) + P(A.C) – P(A.B.C) = 0.019 Rare event approximation P(T) = P(A.B) + P(A.C) = P(A).P(B)+P(A).P(C) = 0.02 University of Strathclyde Business School A
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- How would a T test give us information about if men or women could jump higher in a vertical leap test?4) Suppose John is risk neutral and faces an uncertain outcome in which he loses $ 1000 $1000 with probability p and $0 with probability (1-p) (1-p), and John knows the value of p. John is offered insurance. John's value of this insurance is \40, i.e. his maximum willingness to pay for the insurance is $40. What is the value of p with 0Jamal has a utility function U= w!/2_where W is his wealth in millions of dollars and Uis the utility he obtains from that wealth. In the final stage of a game show, the host offers Jamal a choice between (A) $4 million for sure, or (B) a gamble that pays $1 million with probability 0.6 and $9 million with probability 0.4. a. Graph Jamal's utility function. Is he risk averse? Explain. b. Does A or B offer Jamal a higher expected prize? Explain your reasoning with appropriate calculations. 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O a. n/(pn+1-p) O b. pn/(n+1-p) Oc. pn/(pn+1-p) O d. pn/(pn+n-p) Next page Jump to.. ularI'm have a difficult time understanding how to solve (c). I keep getting the answer wrong. If I unsterstand correctly the probabilty of not being femaleP(A) =1-total #of female/total # of male and female and the probability of not have a degree outside of fieldP(B) is 1-degrees outside of field/ total degrees to solve I did P(A)+P(B)- probability of being female with degree in field. then I tried to solve for probability of being male with a degree in the field and it was still incorrect.When an interval does not include its endpoints (example: “fewer than 5 successes”), you may need to adjust your numbers before entering them into Geogebra. This applies to discrete distributions only! Since a Binomial distributions takes only integer values, “fewer than 5 successes” and “at most 4 successes” are describing the same range of values (and thus the probabilities are the same). Geogebra cannot compute P(X<5)P(X<5), but it will compute P(X≤4)P(X≤4). Keeping n = 20 and p = 0.5 for now, compute the probabilities of the following. Use four decimal places, and do not convert to percent. Fewer than 5 successes: More than 12 successes: Strictly between 8 and 12 successes: At least 7, but fewer than 10 successes:Q1: 1.Please describe the differences and connections between Probability and Statistics. Then explain why we say conditioning is the soul of our course.< 2.Please describe the pros and cons of Bayesian statistical inference and Classical statistical inference. Then explain why conjugate priors are important for Bayesian statistical inference.<There are N sites that need protection (number them 1 to N). Someone is going to pick one of them to attack, and you must pick one to protect. Suppose that the attacker is going to attack site i with probability q;. You plan on selecting a site to protect, with probability pi of selecting site i. The choice of {qi} and {p;} represent the attacker's and defender's strategy, respectively.When a man observed a sobriety checkpoint conducted by a police department, he saw 656 drivers were screened and 5 were arrested for driving while intoxicated. Based on those results, we can estimate that P(W)equals=0.00762,where W denotes the event of screening a driver and getting someone who is intoxicated. What does P(W) denote, and what is its value? What does P(W) represent? P(W)=Another trader would like to carry out a hypothesis test about stocks that offer dividends. Why is this hypothesis test right- tailed?Brian makes many predictions, but only 37% of them come true. The accuracy of the predictions are independent. Jack makes a bet with Joan on the next 4 days about Brian’s predictions. Jack gets 10 dollars when Brian's prediction is correct but loses 5 dollars when Brian is wrong. Let X be the total amount of money won by Jack for every correct prediction of Brian in the next 4 days. Find Jack’s expected earnings, Specify properties of expectations used if any.Let p=(12-2x)^2 for 0≤x≤3 be the price at which x hundred units of a certain commodity will be sold, and let R(x)=xp(x) be the revenue obtained from the sale of the x units. For what level of production is revenue maximized?SEE MORE QUESTIONS