J 1 Problem 1Consider the mixed effects modelY₁ = a + b₁x + σei, with b;= N(μ, 7²).(1) The mean and variance of yi are, respectively,Problem 2With the same model as in Problem 1, prior distributions are assigned to λ = 1/0², nowassumed unknown, and μ, with a and 72 known. The prior for A is gamma(1, 1) and the priorfor μ is N (0, 10²). Using a Gibbs sampler algorithm.(5) If a = 0 and o is known, the posterior distribution for μ is normal with mean and variance (leto² = x² 7² +0²)OO()12²/²+1/10 1²/0²+1/10)Σ₁-13,21/0²-1 2²/0²+1/100 E 2²/0²+1/100ΣπίσηΣ /6+1/100,ਵ

by bartleby policy i can give only one question at time. so ,sorry for 2nd question

Answered: (1) The mean and variance of y, are,…

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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Problems 5 and 6 refer to the discrete random variables X and Y whose joint distribution is given in the following table, so P(X = 1 and Y = -1) = 1/4, P(X = 1 and Y = 1) = 0, etc. Problem 5: Compute the marginal distributions of X and Y, and use these to compute E(X), E(Y), Var(X), and V ar(Y). Problem 6: Compute Cov(X, Y) and the correlation ρ for the random variables X and Y. Are X and Y independent? Y= -1 Y =0 Y =1 X =1 1/4 1/8 0 X =2 1/16 1/16 1/8 X =3 1/16 1/16 1/4
Problem 1. Consider the following density function. f(x )=[ (kx) ^ (2/3) * 0 < x < 2 Find the value of k. Find the cumulative distribution function ( CDF) of X Find the inverse of the CDF. Simulate a random sample of 10000 values from the above distribution by using inversetransformation and find the mean and the variance of those values, and write the Rcode.
Find the cumulative distribution function of the random variable X representing the number of defectives in Problem #5. Then using F(x), find (a) P(X = 1); (b) P(0 < X ≤ 2).
9.1) Suppose X1, X2, and X3, denotes a random sample from the exponential distribution with density function shown in the image. a) Which of the above estimators are unbiased for θ? b) Among the unbiased estimators of θ, which has the smallest variance?
Problem 2-5.5. But change the problem to say Gaussian noise variance of 2, and threshold of 6V.
QUESTION 12 Historically, the proportion of people who trade in their old car to a car dealer when purchasing a new car is 48%. Over the previous 6 months, in a sample of 115 new-car buyers, 46 have traded in their old car. To determine (at the 10% level of significance) whether the proportion of new-car buyers that trade in their old car has statistically significantly decreased, what can you conclude concerning the null hypothesis? Reject the null hypothesis Fail to reject the null hypothesis
Problem 3. Suppose a test for detecting a certain rare disease has been perfected that is capable of discovering the disease in 97% of all afflicted individuals. Suppose further that when it is tried on healthy individuals, 5% of them are incorrectly diagnosed as having the disease. Finally, suppose that when it is tried on individuals who have certain other milder diseases, 10% of them are incorrectly diagnosed. It is known that the percentages of individuals of the three types being considered here in the populations at large are 1%, 96%, and 3%, respectively. Calculate the probability that an individual, selected at random from the population at large and tested for the rare disease, actually has the disease if the test indicates he is so afflicted.
QUESTION 11 An educator estimates that the dropout rate for seniors at high schools in Colorado is 15%. Last year in a random sample of 300 Colorado seniors, 34 withdrew from school. At α = 0.10 level of significance, is there enough evidence to reject the educator’s claim? Yes, because the p-value is 0.075 Yes, because the z-statistic is 1.6 No, because the p-value is 0.038 Yes, because the p-value is larger than 0.15
An analogue signal received at a detector, measured in microvolts, is normally distributed with mean of 185 and variance of 244 If we know the signal is greater than 200 µV, what is the probability that it is in fact greater than 220 µV? Question 8 options: a 0.0534 b 0.0603 c 0.0211 d 0.0743

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(1) The mean and variance of y, are, respectively,