Numerical Maximization: Suppose we want to maximize this likelihood with respect to 3: TI 1 L(B|y₁, yn) = II i=1 -yi/B
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Derive the equation for βi that is used by the Newton algorithm.
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- solveIn random sampling from the exponential distribution, f(x) =1 θθe x− , x > 0, θ> 0, find the maximum likelihood estimator of θ and obtain the asymptotic distribution of this estimatorFormula: Expected value = E(x) = x1P1+x2P2+ ... + xnPn Where x = the outcome and P = probability of outcome Dr. Kimball likes to go fishing with his son. To motivate his son, he pays him for the first fish that he catches. There are two types of edible fish that his son can catch: Trout and Salmon. If he catches a Trout he pays him $5, if he catches Salmon $3. There is a 20% chance that he will catch a trout and 50% that he will catch a Salmon. On average, how much does Dr. Kimball pay his son on a trip?2 Given the exponential distribution: f(x) = {1/θ e^(-x/θ) ; x > 0 0; ew]
- When the HHI is less than 1500, the market price is a competitive one, while, when the HHI is ranging from 1500 to 2500, the market is slightly concentrated. When the value is above 2500, the market is extremely concentrated. Here, for all the 3 years the HHI is above 2500, implying that the market is highly concentrated one. Question Are your conclusions for HHI consistent with the five-firm concentration in all cases? Give two reasons to support your answer.X = max(10,Y) with Y ~ Poisson(lambda=13) a) Calcuate the exact expectation and the variance of X.4- Distribution of velocity (DV) of a molecule is given with the following equation a, b, e, D are constants. Find the the most probable velocity where DV is at maximum
- TF.12 The joint pdf of the lifetimes X and Y in years of two batteries working in parallel is (see picture) a) Find the probability P(Y ≤ 0.5). b) Find the expected values E(X) and E(XY).Economics Now suppose that the time series process {Xt}, is expressed as Xt = z + et where et is iid with a mean of zero and a variance of σ , and the variable z does not change over time (time invariant) which means it has a mean E(z) = 0 and , and it is assumed that z and et are uncorrelated: i. Find the mean xt , E(Xt) and the variance Xt, var(Xt). Do they depend on t? ii. Determine the covariance of xt and xt+h for h > 0, Cov(Xt , xt+h) iii. Is xt stationary? Explain.SohnCo has a division that manufactures steel for construction uses. Recently, they have had someproblems with their steel and look into some failures. The most probable strength of a steel beam isgiven by 24Y ―0.05 kips where Y is the number of cycles. This value is known to 25% with 90%confidence.a) How many cycles will elapse before the beam loses 20% of its strength?b) Suppose the cyclic load on the beam is 10 kips. How many cycles will occur before the probability offailure reaches 10%. Assume this can be described by a lognormal distribution.
- T2.9 The waiting time X in minutes for an order at Burger King has exponential distribution with parameter sigma = .25. a) Find the probability that the waiting time for an order exceeds 7 minutes. b) Find the probability that the waiting time for an order is between 2 and 8 minutes, inclusive.Example 3: BPA in Tomato Soup A consumer protection agency is testing a sample of cans of tomato soup from a company. If they find evidence that the average level of the chemical bisphenol A (BPA) in tomato soup from this company is greater than 100 ppb (parts per billion), they will recall all the soup and sue the company. a). State the null and alternative hypotheses. b). What does a Type I error mean in this situation?Insurance A 65-year-old woman takes out a $100,000 term life insurance policy. The company charges an an-nual premium of $520. Estimate the company’s expected profit on such policies if mortality tables indicate thatonly 2.6% of women age 65 die within a year.