**Problem 13: Statistical Estimation**Given: A random sample $ Y_1, Y_2, \ldots, Y_n $ from a population with the probability density function (pdf)\[f(y|\theta) = (\theta + 1)y^\theta, \quad 0 < y < 1, \quad \theta > -1\]**Tasks:**a) **Find an estimator for $\theta$ by the method of moments.**b) **Find the maximum likelihood estimator for $\theta$.**

Let Y 1, Y2, - - - - - - -, Yn denote a random sample from a population with pdf f (y/θ) = (θ+1)…

. Let Y,, Y2, .. , Y, denote a random sample from a population with pdf fyle) = (0 + 1)y®,0 < y < 1,0 > -1 a) Find an estimator for theta by the method of moments. b) Find the maximum likelihood estimator for theta.

. Let Y,, Y2, .. , Y, denote a random sample from a population with pdf fyle) = (0 + 1)y®,0 < y < 1,0 > -1 a) Find an estimator for theta by the method of moments. b) Find the maximum likelihood estimator for theta.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

12 13 14 15 16 17 18 19 20 21 22 23 24 25 H Movie Ticket Prices 4 5 5 B 6 10 11 Cost Of Ticket Which of the following is the best measure of center for the data shown, and what is that value? O The mean is the best measure of center and equals 11. O The mean is the best measure of center and equals 11.5. O The median is the best measure of center and equals 11. O The median is the best measure of center and equals 11.5.
a) Let X₁, X₂, X3,..., X, be a random sample of size n from population X. Suppose that X~N(0, 1) you and Y = -√n. VR i) Show that the standard score of the sample mean X, is equal to Y. ii) Show that the mean and variance of the random variable Y are 0 and 1, respectively. iii) Show using the moment generating function technique that Y is a standard normal rando... variable. iv) What is the probability that Y² is between 0.02 and 5.02? b) Let X₁, X₂, X, and Y₁, Y₂.... Y be random samples from populations with moment generating functions Mx, (t) = eat+t² and My (t) = (-), respectively. 25 i) Find the sampling distribution of the statistic W = X₁ + 2X₂ X3 + X₁ + X5. ii) What is the value of the sample size n, if PIX(X-X)2> 68.3392] = 0.025? iii) What is the value of the sample size m, if P(|Y-Hy ≥10) <0.04? QUESTION A
Please solve with the step max in 60-90 minutes the chapter actuarial Investigate whether the risk measure Variance principle premium p(L) = μL + ασL2 α = loading factor meets the axioms (T, S, PH and M)
For 50 randomly selected speed dates, attractiveness ratings by males of their female date partners (x) are recorded along with the attractiveness ratings by females of their male date partners (y); the ratings range from 1 to 10. The 50 paired ratings yield x = 6.4, y = 5.9, r= - 0.319, P-value = 0.024, and y = 8.29 – 0.379x. Find the best predicted value of y (attractiveness rating by female of male) for a date in which the attractiveness rating by the male of the female is x = 8. Use a 0.10 significance level. ..... The best predicted value of y when x= 8 is (Round to one decimal place as needed.)
For 50 randomly selected speed dates, attractiveness ratings by males of their female date partners (X) are recorded along with the attractiveness ratings by females of their male date partners (y); the ratings range from 1 to 10. The 50 paired ratings yield x=6.2, y = 5.9, r= -0.244, P-value = 0.087, and y =7.68 - 0.285x, Find the best predicted value of y (attractiveness rating by female of male) for a date in which the attractiveness rating by the male of the female is x= 4. Use a 0.05 significance level. The best predicted value of y when x = 4 is (Round to one decimal place as needed.)
For 50 randomly selected speed dates, attractiveness ratings by males of their female date partnerS (x) are recorded along with the attractiveness ratings by females of their male date partners (y); the ratings range from 1 to 10. The 50 paired ratings yield *= 6.3, y = 6.1. r= - 0.283, P.value = 0.046, and g = 8.39 - 0.369x. Find the best predicted value of y (attractiveness rating by female of male) for a date in which the attractiveness rating by the male of the female is x= 4. Use a 0.01 significance level. see score The best predicted value of g when x= 4 is 7. (Round to one decimal place as needed.)
Suppose claim amounts at a health insurance company are independent of one another. In the first year calim amounts are modeled by a gamma random variable X with alpha=40, and beta=3. In the second year, individual claim amounts are modeled by random variable Y=1.05X+3. Let W be the average of 30 claim amounts in year two set up the equation to model the random variable W. a) Find the moment generating function of W b) Based on moment generating function of W is W also a gamma distribution? if so what are the parameters? c) Find the approximate probability that W is between 125$ and 130$.
For 50 randomly selected speed dates, attractiveness ratings by males of their female date partners (x) are recorded along with the attractiveness ratings by females of their male date partners (y); the ratings range from 1 to 10. The 50 paired ratings yield x = 6.4, y = 6.0, r=-0.233, P-value = 0.104, and ŷ= 7.88 -0.292x. Find the best predicted value of y (attractiveness rating by female of male) for a date in which the attractiveness rating by the male of the female is x = 4. Use a 0.01 significance level. The best predicted value of y when x = 4 is (Round to one decimal place as needed.)
Let X1,., Xn all be independent exponential distributions all with the same parameter 2. What is the distribution of the minimum of (X1,. a) what is the distribution of the smallest order statistic Y, ? b) Specify both the pdf of the distribution and describe the distribution and its parameters. ,Xn)? In other words:
Derive the following:(c) variance(d) moment generating function
For 50 randomly selected speed dates, attractiveness ratings by males of their female date partners (x) are recorded along with the attractiveness ratings by females of their male date partners (y); the ratings range from 1 to 10. The 50 paired ratings yield x=6.4, y= 6.0, r= -0.124, P-value = 0.391, and y = 6.95-0.146x. Find the best predicted value of y (attractiveness rating by female of male) for a date in which the attractiveness rating by the male of the female is x = 7. Use a 0.10 significance level. The best predicted value of y when x 7 is. (Round to one decimal place as needed.)
Parametric Confidence Interval