We observe a sequence of independent identical trials with two possible outcomes on eachtrial, S and F, and with P(S) = p. The number of the trial on which we observe the sixthsuccess, Y has a negative binomial distribution with parameters r = 6 and p. Suppose that weobserve the sixth success on trial number 10. Show that p =3is the value that maximizesP(Y= 10).

Given Information: There are two possible outcomes of each trial S and F where S is the success and…

Answered: We observe a sequence of independent…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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In a continuous-time surplus model, the claim severity is distributed as BN(2, 0.4). Determine the Lundberg upper bound for the probability of ultimate ruin if the initial surplus is 2 and the prIn a continuous-time surplus model, the claim severity is distributed as BN(2, 0.4). Determine the Lundberg upper bound for the probability of ultimate ruin if the initial surplus is 2 and the premium loading factor is 0.25.emium loading factor is 0.25.
An elephant eats an average of 3 bushels of alfalfa per day, with a standarddeviation of 0.8 bushels. Suppose that you need to feed 10 elephants for oneweek. If the distribution is normal, what is the minimum number of bushels ofalfalfa so that there is no more than a 10% chance of running out by the end of the week?
You and two other people are to place bids for an object, with the high bid winning. If you win, you plan to sell the object immediately for 10,000.(a) How much should you bid to maximize your expected profit if you believe that the bids of the others can be regarded as being independent and uniformly distributed between 7,000 and 10,000?
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Hubert has difficulty finding parking in his neighborhood and, thus, is considering the gamble of illegally parking on the sidewalk because of the opportunity cost of the time he spends searching for parking. On any given day, Hubert knows he may or may not get a ticket, but he also expects that if he were to do it every day, the average amount he would pay for parking tickets should converge to the expected value. If the expected value is positive, then in the long run, it will be optimal for him to park on the sidewalk and occasionally pay the tickets in exchange for the benefits of not searching for parking. Suppose that Hubert knows that the fine for parking this way is $100, and his opportunity cost (OC) of searching for parking is $20 per day. That is, if he parks on the sidewalk and does not get a ticket, he gets a positive payoff worth $20; if he does get a ticket, he ends up with a payoff of$___.Given that Hubert does not know the probability of getting caught, compute his…
Suppose model (XY, XZ, YZ) holds in a 2 x 2 x 2 table, and the common XY conditional log odds ratio at the two levels of Z is positive If the XY and YZ conditional log odds ratios are both positive or both negative, show that the XY marginal odds ratio is larger than the XY conditional odds ratio.
Texas Instruments produces computer chips in production runs of 1 million at a time. It has found that the fraction of defective modules can be very different in different production runs. These differences are caused by small variations in the set-up of each production run. Managers have observed that defective rates are roughly triangular, with a lower bound of 0%, and an upper bound of 50%. Defects more likely to be near 10% than any other single value in their range. Now suppose that we have taken a sample of 10 modules, and 2 of them are defective. i. What is the conditional probability of a defective rate less than 25% in this production run?ii. For what number M would you say that the defective rate is equally likely to be above or below M?
If you have a set of samples S= 0, 0, 1, 0, 1, 0 from a binomial distribution where P(x + 0) = 1ji and P(x = 1) = mu , the maximum likelihood estimate of u is
The swing (difference between the maximum and minimum values) of S&P500 on any one day is distributed with pdf f1(x) = 2 20(1+x/20)3 , x > 0 if the market that day is “stable” or as f2(x) = 2 200(1+x/200)3 if the market is “volatile”. A market analyst assigns a 10% chance for Apr 29, 2013 being “volatile”. The analyst believes that the market state (stable/volatile) of a day persists the next day with probability 0.9 or switches to the other state with probability 0.1. The loss associated with flagging Apr 30, 2013 as “volatile” (flag V) or “stable” (flag S) are given below. Truth about Apr 30, 2013 ‘Volatile’ ‘Stable’ Flag V 0 1 S 10 0 Should the analyst flag Apr 30, 2013 as “stable” if a swing of 20 is recorded on Apr 29, 2013? Justify your answer.
I need help finding the Maximum Likelihood estimator of Y1,Y2,...,Yn with a random sample size n from an exponential distribution with parameter β.
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