B4. Let X1, X2, ..., X, be a random sample from a normal distribution with known meanµ, unknown variance o? and density function1fx(x)IER.V2no2Using the log-likelihood, find the maximum likelihood estimator for o?. If the mean isµ = 3 and the sample is {r1, 2, T3} = {-1.2,0.5, 1.5}, what is the estimate for o??

Given that X1, X2, ..., Xn be a random sample from a normal distribution with known mean μ, unknown…

Answered: B4. Let X1, X2, ..., X, be a random…

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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A professor grades on a curve by assigning C's to all scores from u- ; to u+%, B's to all scores from i+% to µ+ , and D's to all scores from u – * to µ – 5. Everyone who scores below a D gets an F, and everyone who scores above a B gets an A. a. If the scores are normally distributed with mean u and variance o², what percentage of students will receive each grade? Hint: convert to z-scores and use pnorm() to find probabilities (percentages) b. If the scores are uniformly distributed (continuous) from 0 to 100 what percentage will receive each grade? Hint: first determine the values of u and o for this distribution
Let X. X , be a random sample of siren from a normal distribution with population mean 0 and population variance a>Ois unknown, that is N(0, ). Suppose that we define the following plvotal quantity (n-1)s where & and S' are the sample mean and the sample variance, respectively. Use the plvotal quantity (Q) to derive the (1- a) 100% confidence interval (C) for the unknown parameter (o) if the two critical values are q--n, a) and (n-1) (A) CI = (n8+(n-1)51 + n-1) s (8) CI - (C) CI - + (n-1) s (D) CI= O D O A O c O B
Daily sales of a store is normally distributed with mean μ=180 Rials and variance σ2 =100. Find the probability that total sales over a period of nine days is more than 1800 Rials.
i need help with c
Let Y, represent the ith normal population with unknown mean #, and unknown variance of for i=1,2. Consider independent random samples, Ya, Ya, Yin, of size n,, from the ith population with sample mean Y, and sample variance S² = (₁-P) ². (d) Define V₁, a function of S1, that has a chi-square distribution. (e) Is V₁ a pivotal function to find a confidence interval for o?? Explain with argument. (f) Find a (1-a) x 100% confidence interval for of
This exercise requires the use of a graphing calculator or computer programmed to do numerical integration. The normal distribution curve, which models the distributions of data in a wide range of applications, is given by the function 1 p(x) = e (x - 1)?/(202), V 2n 0 where n = 3.14159265... and o and u are constants called the standard deviation and the mean, respectively. Its graph (for o = 1 and u = 2) is shown in the figure. f(x) 0.3 0.2 0.1 3 4 5 With o = 3 and u = 0, approximate p(x) dx. (Round your answer to four decimal places.)
If the random variable X as a mean of u and a variance of o2 what is the P((X-u)² < 20): O less that equal to 1/4 O greater than or equal to 3/4 cannot tell O equal to 5/4
With an American penny, the likelihood of getting H when it is spun on edge is 0.3. If X is the random variable where X(H ) = 1, X(T ) = −1, find the expected value E(X), the variance, Var(X), and express X in its standard form.
If X is a negative binomial rv, then Y= r+Xis the total number of trials necessary to obtainr S’s. Obtain the mgf of Y and then its mean valueand variance. Are the mean and variance intuitively consistent with the expressions for E(X)and V(X)? Explain
let Y=5X+10 and X be normally distributed with a mean 10 and varience 25. find P(Y<54).
The Volatility X for the S&P stock index on a given day is a normal random variable with mean = 10 and standard deviation = 2 The volatilities recorded over a 100-day period on the S&P500 are Y1, Y2, ... Y100. Assume that these Yi's are independent and identically distributed, uniform on the interval [5,15]. Let V = (Y1 + Y2 + ... + Y100)/100. What approximately is P[9.5 < V < 10.5]?
The random variable x has a normal distribution with mean 50 and variance 9. Find the value of x, call it x0, such that: a) P(x ≤ xo) = 0.8413 b) P(x > xo) = 0.025 c) P(x > xo) = 0.95 d) P(41 ≤ x ≤ xo) = 0.8630

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