a) & b) Your friend transmits an unknown value to you over a noisy channel. Thenoise is normally distributed with mean 0 and a known variance 4, so the value x thatyou receive is modeled by N(0,4). Based on previous communications, your prior onis N (5,9).(a) Suppose your friend transmits a value to you that you receive as x = 6. Show thatthe posterior pdf foris N(74/13, 36/13). For this problem, you need to derivethe posterior by carrying out the calculations from scratch.(b) Suppose your friend transmits the same value to you n = 4 times. You receivethese signals plus noise as ₁,..., with sample mean = 6. Using the same priorand known variance o² as in part (a), show that the posterior on 0 is N(5.9,0.9).Plot the posterior and posterior on the same graph. Describe how the data changesyour belief about the true value of 0. For this question, you may use the normalupdating formulas.

Answered: Image /qna-images/answer/d0f34ef1-ed0f-4186-a6b8-b0eb7f8b43c0.jpg

Answered: nally distributed with mean 0 and a…

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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An auto manufacturer claims that the variance of the gas mileage in a model of a hybrid vehicle is 0.16. A random sample of 30 vehicles has a variance of 0.26. At alpha = 0.05, is there enough evidence to reject the claim? Assume the population is normally distributed.
The average number of pounds of sliced ham ordered per customer at the deli where Dennis used to work was 1.4, but at his new job, the average of the 32 people who have ordered ham so far is 1.5 pounds, with a standard deviation of 0.3 pounds. a) Write the null and alternative hypotheses to test if the average amount of ham bought is higher at the new store. H0:μ= H1:μ> b) For α=0.025, find the rejection region in terms of z. [Write your answer with 2 decimal places.] R:z≥ c) What test statistic corresponds to an x¯ of 1.5 pounds? [Round your answer to 2 decimal places.] z= d) Should you reject the null hypothesis?
It is known that the volume of containers of a specific lubricant is normally distributed with a variance of 0.03 liters. Test the hypothesis that o^2 is not equal to 0.03 for the random sample of 10 containers with s = 0.24585 l. Use a P-value in your conclusions. Note:In the image, this is the exercise in Spanish, which is the original, to make it more understandable.
An auto manufacture claims that the variance of the gas mileages in a model of hybrid vehicle is 0.16. A random sample of 30 vehicles has a varience of 0.26. At a=0.05 is there enough evidence to reject the claim??
An analogue signal received at a detector, measured in microvolts, is normally distributed with mean of 185 and variance of 244. What is the probability that is the signal will be less than 203 µV given that it is less than 184 µV?
Suppose your waiting time for a bus in the morning is uniformly distributed on [0, 10], whereas waiting time in the evening is uniformly distributed on [0, 12] independent of morning waiting time. (a)If you take the bus each morning and evening for a week, what is your total expected waiting time? (Assume a week includes only Monday through Friday.) [Hint: Define rv's X1,... , X10 and use a rule of expected value.] Total Time= min (b) What is the variance of your total waiting time? (Round your answer to two decimal places.) Variance of Wait Time= min2 (c) What are the expected value and variance of the difference between morning and evening waiting times on a given day? (Use morning time − evening time. Round the variance to two decimal places.) expected value = min variance= min2 (d) What are the expected value and variance of the difference between total morning waiting time and total evening waiting time for a particular week? (Use morning time −…
Suppose a continuous random variable X pdf constant from 0 to 7.516, where the pdf is zero elsewhere. what is variance of this random variable?
The time at which a bus arrives at a station is uniform over an interval (a,b) with mean 2:00 pm and variance 12 minutes. Determine the values of a and b.

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