Let X₁, X₂,..., X, be a random sample from a Pareto (1, B) population, i.e., the population pdf is given bynƒ(xß) = P₁, 1. There is no need to find to so that the size of

a) To show that ∑i=1nlnXi is sufficient for β, we need to show that the likelihood function L(β|x)…

Answered: Let X₁, X₂,..., X be a random sample…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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-; Consider Y1,Y2.Yıs are a random sample from a normal distribution with an unknown mean u, and population standard deviation o = 8.4. Suppose the hypothesis of interest are Ho:H = 39 HA:H > 39 with rejection region RR = Y > 42.8. a) What is the distribution of Y assun.ng Ho is true? b) Calculate the type I error a. c) Calculate the type Il error B when u = 41.3.
You decide to play K number of video games, where K is a Poisson random variable with parameter A. Assume that time you spend on a video game k = 1, 2,..., K has a normal distribution with mean µg and variance of. Also assume that µk >> 0 and of is small, so that you can neglect negative time values. Let T be the total time you spend on playing video games, compute the mean and variance of T.
a. Let Z ~ Normal(0, 1) be a continuous standard normal random variable with mean of 0 and standard deviation of 1. What is the probability that Z comes out to be less than -1.64? Normal(26.2, 5) is a continuous normal random variable 26.2 and standard deviation of o = 5. What is the probability that b. Suppose instead that X ~ with mean of µ = X comes out to be less than 18? c. Working still with X That is, find a value c such that the probability that X is bigger than c is 2.5%. Normal(26.2, 5), find a value c such that P(X > c) = 0.025.
Suppose that Y₁, Y₂, ..., Ym is a random sample of size m from Gamma (a = 3, B = 0), where 0 is not known. Check whether or not the maximum likelihood estimator Ô is a minimum variance unbiased estimator of the parameter 8.
Use a t-test to test the claim about the population mean y at the given level of significance a using the given sample statistics. Assume the population is normally distrbuted Claim: jI * 25; a = 0.01 Sample statistics: × = 25.1, s = 4.2, n= 11
Calculate the value of the unpooled test statistic t in each of the following situations. In each case, assume the null hypothesis is Ho: H, - H, = 0. (Ro (a) x, = 38, s, = 8, n, = 64; x2 = 36, s2 = 7, n, = 49 t = (b) The difference in sample means is 43, s.e.(x, - x2) = 27.
This column contains data x1, . . . , xn, which is assumed to be a sample from a normal distribution N(µ, σ 2 ). For this sample, find the maximum likelihood estimates µˆ and σˆ.
Past research has indicated that the average age of death row inmates is 41 years old. researcher would like to determine if the average age has changed. She randomly selects 50 death row inma s and ds their average age to be 37 years old. The hypothesis the statistician wants to test is: a. Ho: µ=37 vs_ Ha: µ ± 41. b. Ho: µ=41 vs Ha: µ< 41. Ho: u = 41 vs. H: u 41 d. Ho: µ=37 vs_Ha: µ< 41. C. 2. If a player at a casino is playing roulette and betting on red, there is a 18 / 38 or 0.474 chance that he will win on any spin of the roulette wheel. If we take a random sample of 300 players betting on red, then p is the proportion of times that the player wins. What is the mean of the sampling distribution of p? t' a. b. What is the standard deviation (os) of the sampling distribution of p? c. If repeated samples of 300 players are taken, what would be the range of the sample proportion of players victories according to the 95 part of the 68-95-99.7 rule" pts) 3. The z statistic for a…
Let X~Geo(0.3). Find the following a. P(X = k). b. P(1 ≤ X 3) and describe its interpretation. d. The mean μ = E(X) and the Variance σ2 = Var (X) of the random variable X.
A study of parental empathy for sensitivity cues and baby temperament (higher scores mean more empathy) was performed. Let x, be a random variable that represents the score of a mother on an empathy test (as regards her baby). Let x, be the empathy = 68.36. Another random sample of 31 fathers gave score of a father. A random sample of 37 mothers gave a sample mean of x, X, = 60.06. Assume that o, = 11.55 and o, = 11.45. (a) Let u, be the population mean of x, and let u, be the population mean of x,. Find a 99% confidence interval for u, - Hz. (Round your answers to two decimal places.) lower limit upper limit (b) Examine the confidence interval and explain what it means in the context of this problem. Does the confidence interval contain all positive, all negative, or both positive and negative numbers? What does this tell you about the relationship between average empathy scores for mothers compared with those for fathers at the 99% confidence level? Because the interval contains only…
Let Y1, Y2, Y3 denote independent exponential random variables with respective rates A; for i e {1,2, 3}. Answer the following questions; (a) Compute E[Y1 +Y2 +Y3]Y1 > 1, Y2 > 2, Y3 > 3]. Your answer should be an expression using A;'s. (b) Compute the probability that Yı is the smallest among three random variables. Hint: P(X < Y) = S" Px,y (x, y)dædy where Px,Y (x, y) is the joint density function.
Can I get help with parts a),b) and c)

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Let X₁, X₂,..., X be a random sample from a Pareto (1, ß) population, i.e., the population pdf is given by n f(x|B)=₁₁1 ß. There is no need to find to so that the size of the test is a. n In X, ~ gamma (n,1/ß).