Taking expectation of a Wiener process wich is normally distrubuted with n(0,1) what is the value of that expectation?
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Taking expectation of a Wiener process wich is normally distrubuted with n(0,1) what is the value of that expectation?
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- Population Genetics In the study of population genetics, an important measure of inbreeding is the proportion of homozygous genotypesthat is, instances in which the two alleles carried at a particular site on an individuals chromosomes are both the same. For population in which blood-related individual mate, them is a higher than expected frequency of homozygous individuals. Examples of such populations include endangered or rare species, selectively bred breeds, and isolated populations. in general. the frequency of homozygous children from mating of blood-related parents is greater than that for children from unrelated parents Measured over a large number of generations, the proportion of heterozygous genotypesthat is, nonhomozygous genotypeschanges by a constant factor 1 from generation to generation. The factor 1 is a number between 0 and 1. If 1=0.75, for example then the proportion of heterozygous individuals in the population decreases by 25 in each generation In this case, after 10 generations, the proportion of heterozygous individuals in the population decreases by 94.37, since 0.7510=0.0563, or 5.63. In other words, 94.37 of the population is homozygous. For specific types of matings, the proportion of heterozygous genotypes can be related to that of previous generations and is found from an equation. For mating between siblings 1 can be determined as the largest value of for which 2=12+14. This equation comes from carefully accounting for the genotypes for the present generation the 2 term in terms of those previous two generations represented by for the parents generation and by the constant term of the grandparents generation. a Find both solutions to the quadratic equation above and identify which is 1 use a horizontal span of 1 to 1 in this exercise and the following exercise. b After 5 generations, what proportion of the population will be homozygous? c After 20 generations, what proportion of the population will be homozygous?Find the moment generating function of the continuous random variable X∼U (a, b).Let P be a random variable having a uniform distribution with minimum 0 and maximum 3 i.e. P ~ Uniform(0, 3). Let Q = log (P/(3-P)). Find E[P]. You areexpected to solve this problem without using Method of Transformation.
- Let X be a Poisson random variable with parameter k. (a) Show that the moment generating function for X is given by ?? (?) = ?^(?(?^?−1)) (b) Show that E(X) = k. (c) Show that Var (X) = k.Probability and Stochastic Process Identify for the following 13.3 13.4 13.5 13.6 whether the process is discrete time or continuous time, discrete or continuous value5. Let Y1, . . . , YN be a random sample from the Normal distribution Yi ∼ N(ln β, s2) where s2is known.Find the maximum likelihood estimator of b from first principles.Find the Score function, the estimating equation and the information matrix.
- The number of requests for assistance received by a towing service is a poisson process with rate α = 2 per hour. After realizing that he did not miss any calls for assistance when taking a 15 minute break, the operator decides to take another 15-minute break. What is the probability that he will not miss any calls again? We want to determine P[no calls in time interval (0 , 1/2)│no calls in time interval (0 , 1/4)], where the unit used for time interval is hours.Let X and Y be two jointly Gaussian real random variables, each with zero mean,variance 1, and correlation coefficient ρ ∈ (0, 1). Let a, b ∈ R be such that a2 + b2 = 1, and defineW := aX + bY .a. Find values for a and b to maximize the variance of W . Hint: Use eigendecomposition.b. Does the optimal W (from part a) have a probability density function? If yes, derive it. Ifnot, explain why.Using R, run simulated annealing for a 2 parameter cauchy distribution (with beta constrained to 0.1, so only a single parameter alpha remains) and the negative log-likelihood curve for alpha has serval optima. show a summary graph of the values of alpha visited during the algorithm and how they relate to the position of the optima. data of the cauchy distribution are x<- c(-4.20, -2.85, -2.30, -1.02, 0.70, 0.98, 2.72, 3.50)
- If it is known that the random process X (t) is a stationary process in a broad sense, could the following autocorrelation function belong to this process? Explain the reason for your answer.Let X and Y denote two discrete random variables taking the values in x andy respectively. The collected data over time is represented in the following stochastic model. Are the X and Y independent? ExplainFind the moment generating function of the continuous random variable X∼U (a, b).Please give me the all details
