统计练习题代写 Stats 426代写

Practice Problems Stats 426

统计练习题代写 Here are some problems to try in addition to homework, quiz, and midterm problems. 1) Let Y1, Y2, . . . Ynbe iid from the density function

Here are some problems to try in addition to homework, quiz, and midterm problems.

1)

Let Y₁, Y₂, . . . Y_nbe iid from the density function

Without any calculations, use what you know about the chi-square and F distributions to find the distribution of X₁/X₂.

3) 统计练习题代写

Recall the Hardy-Weinberg problem described in your text (page 273-274). The multinomial distribution for random variables Y₁, Y₂, Y₃(can extend to more than 3) is given by

where y₁ + y₂ + y₃ = n and the parameters p1, p2, p3 are subject to the constraint p₁ + p₂ + p₃ = 1. This distribution is an extension of the binomial distribution. In fact, the distribution of each Y_i, i = 1, 2, 3 is binomial. So, for example, E[Y₁] = np₁ and V ar(Y₁) = np₁(1−p₁). If gene frequencies are in equilibrium, the genotypes AA, Aa, and aa occur in a population with proportions

p₁ = (1 − θ)² , p₂ = 2θ(1 − θ) , and p₃ = θ²

according to Hardy-Weinberg law.

a) Using the multinomial as the likelihood and a prior distribution of θ ∼ Beta(10, 10), find the Bayes estimator of θ. That is find E[θ|y].

b) Is the Bayes estimator unbiased?

4) 统计练习题代写

Consider the following probability model:

Likelihood : Y₁, . . . , Y_n independent and identically distributed Poisson(θ) Prior : θ ∼ Gamma(α, λ) , α , λ fixed

a) Find the posterior distribution p(θ | y).

b) Find E[θ | y] and V ar(θ | y).

c) Find the marginal distribution p(y). Note that this is the joint discrete distribution

P(Y₁ = y₁, Y₂ = y₂, . . . , Y_n = y_n). (This distribution will be conditional on α and λ).

For any Y_i , i = 1, . . . , n, find E[Y_i] and V ar(Y_i).

6) 统计练习题代写

The data below shows the average weight of varsity football players at the University of Texas for selected years. Fit a linear model of the form (use R code given in Lecture Notes, no need to do by hand)