Write down the log-likelihood function for the problem and obtain an analytical solution for the Maximum Likelihood 1270²1-1/2e-(x-µ)²/20² əIn L(X) Əx = 0
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- Please help me find likelihood, log-likelihood and MLEs of two parameters, thank you.Suppose X1,...,Xn are measurements of the mass of an object. The measurements are normally distributed, with mean equal to mu , the mass of the object, and standard deviation equal to 1 microgram. Find (a) The likelihood function. (b) The log-likelihood function (c) the maximum likelihood estimator for the unknown parameter, andSuppose that an item has a hazard rate function X(t) = 2.4t², t> 0. What is the probability that (a) the item survives to age 0.5? (b) the item's lifetime is between 1.5 and 3? (c) a (-year-old item will survive to age 3?
- For the optimization of the likelihood function, the computation of the log-likelihood L(0; y) = log L(0; y) is more convenient becauseShow that the conditional variance can be written as σ^2 (X) = E { Y^2 | X} −(E[Y | X])^2 no handwritten solution.At the end of summer, the total weight of seeds accumulated by a nest of seed-gathering ants will vary from nest to nest. If the total weight of seeds accumulated by a nest is exponentially distributed with parameter λ = 1/5, (a) What is the probability that the total combined weight of the seeds gathered by 100 nests will be larger than 4 95 pounds by the end of next summer? (b) What is the probability that the average weight of the seeds gathered by the 100 nests is larger than 5.3 ? (c) What assumptions are you making to answer parts (a) and (b)? Do you think those assumptions make sense in the context of this problem? Explain. (d) Tell us about the possibility that the total combined weight of the seeds gathered by 2 nests follows a normal distribution. Justify your answer in the specific context of this problem (ants, nests, seed-gathering). That is, do not just make generic statements that you think apply to every context in the world.
- When I go swimming, the distance in meters that I can swim before getting cramp in one of my hands is exponentially distributed with parameter ?=1/313.3λ=1/313.3. What is the probability that, on a random occasion when I go swimming, I swim at least 593.3593.3 meters without getting hand cramp?Give your solution accurate to 4 decimal places.The pdf is given as follows: f(x) = { (1/6)e^(1/6x) ; x > 0 0; ew] (i) Find the mean and variance of X using the pdf. (ii) Find the moment generating function of X. (iii) Find the mean and variance of X using the moment generating function.Given the pdf: f(x) = { (1/6)e^(1/6x) ; x > 0 0; ew] (i) Find the mean and variance of X using the pdf. (ii) Find the moment generating function of X. (iii) Find the mean and variance of X using the moment generating function.
