Theorem (Cramer-Rao Lower Bound) If is an unbiased estimator of 0 ER then Var() ≥ ¹. The MI lever
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please teach this I do not no notations
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- Signal-to-Noise Ratio: If random variable X has mean μ ¹ 0 and standard deviation s > 0, the ratio r = |μ| /s is called the measurement signal-to-noise ratio (SNR) of X (sometimes SNR is defined as the square of this quantity.) The idea is that X can be expressed as X = μ+ (X − μ), with μ representing a deterministic constant-valued “signal”, and (X − μ) the random zero-mean “noise.” In applications, it is desirable to have an upper-bound, with a probabilistic guarantee, on the magnitude of the relative deviation of X from its mean μ, defined as D = |(X − μ) /μ| . That is, we are interested in finding a positive number a, such that P(D ≤ a) ≥ c where c is a pre-specified number representing our confidence in the upper-bound. If r = 10, provide an upper-bound a, with confidence level c = 0.95.Women executives A company is criticized because only13 of 43 people in executive-level positions are women.The company explains that although this proportion islower than it might wish, it’s not surprising given thatonly 40% of all its employees are women. What do you think? Test an appropriate hypothesis and state your con-clusion. Be sure the appropriate assumptions and condi-tions are satisfied before you proceed.In a Right Tailed Hypothesis test, the test statistic was found to be Z=2.74The rejection region included values greater than the critical value Zc=2.02 The conclusion would be to... Reject the null hypothesis because the test statistic is NOT in the rejection region Fail to reject the null hypothesis because the test statistic is in the rejection region Fail to reject the null hypothesis because the test statistic is NOT in the rejection region Reject the null hypothesis because the test statistic is in the rejection region Accept the null hypothesis because the test statistic is NOT in the rejection region
- a man is investigating the populaion of bear in two areas. Area 1 and Area 2. He expect the number of bear to be X and Y in area 1 and area 2 to be Poisson- distributeted. He expect the number og bear to be λ1 = 3 in area 1 and λ2 = 5 in area 2. Find P(X = 2) and P(X ≥3) and find an approximate value expression for P(X = Y)A company is considering a project which has three options. The payoffs are shown in the body of thetable. In this instance, the payoffs are in terms of present values, which represent equivalent currentdollar values of expected future income less costs. This is a convenient measure because it places allalternatives on a comparable basis. If a small facility is built, the payoff will be the same for all threepossible states of nature. For a medium facility, low demand will have a present value of $7 million,whereas both moderate and high demand will have present values of $12 million. A large facility willhave a loss of $4 million if demand is low, a present value of $2 million if demand is moderate,and a present value of $16 million if demand is high.The payoff table depicting revenues and is shown in the following table. (a) Which alternative should the manager choose under the maximax criterion? (b) Which option should the manager choose under the maximin criterion? (c) Which option…Gaben wants to investigate first if gender is associated with whether the student exhibits excessive hours in playing online games. In his research, a student is said to exhibit excessive gaming if he/she plays for more than 10 hours per week. The following results were obtained. The assumptions of the Chi-square test of independence were __________. Based on the p-value of _______, there is ___________ evidence to say that there is an association between whether the student exhibits excessive gaming or not and his/her gender. Moreover, the Cramer’s V value of _____________ indicates that there is a _________________ association between the two variables.
- Solve for the moment generating function of X if for all natural number n, X ∼ U {1,2,…,n}.A club recruit members either through active recruitment by its current members or through advertising in neighborhood billboards. Suppose that each member of the club recruit new members at a rate of 3 members per week and that advertising in neighborhood billboards generate new members at a rate of 2 members per week. Suppose further that each member is expected to stay a club member for 1 week, on average. Assume that the number of members of the club at any given time follows a birth and death process. Given that the club started with 5 members, what is the expected number of club members after the first two weeks?The ELISA test is used to screen donated blood for the AIDS virus. It is estimated that 0.5% of the population is infected by the AIDS virus. The accuracy of the test is 97.7%; that is, a sample with the AIDS virus is correctly identified to be carrying the virus 97.7% of the time [P(POSITIVE | AIDS) = 0.977]. The specificity of the test is 92.6%; a healthy blood sample is correctly diagnosed 92.6% of the time [P(NEGATIVE | NO AIDS) = 0.926]. Using BAYES THEOREM: Starting with a population of 1,000,000 bottles of donated blood, find the number of bottles in each of the following four categories: AIDS Infected which tested POSITIVE AIDS Infected that tested NEGATIVE NO AIDS Infected that tested POSITIVE NO AIDS Infected that tested NEGATIVE. Discuss the false positive and false negative results. Should ELISA’s credibility be questioned?
