Consider an object that is equally likely to switch temperature readings, under different conditionsbetween any of the seven values l4, i = 0,1,..,6, in the diagram below at any instant t. Let Y be thetemperature reading of the object at any instant t 2 0.L4Ls(1) What are the values of the random variable Y? What is the pmf or pdf of Y?(2) What is the expected temperature of the object at any time?(3) Find the mgf of the random variable Y.

Given: Object is equally likely to switch readings between any of the 7 values Y is the temperature…

Answered: Consider an object that is equally…

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 population with u = 45 and o = 10 is standardized to create a new distribution withu= 100 and o = 20. In this transformation, a score of X = 15 from the original distribution will be transformed into a score of X =.
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Q. 1 In University of Nizwa, you pass an exam if marks is 60 or more out of 100. Suppose the grade your total distribution of STAT210 follows normal (Gaussian) distribution with X~Normal(µ = 70,0² = 16). (i) Find the probability of passing the exam of STAT210. (ii) Given that your grade is greater than 50, find the probability that you pass the exam?
Suppose you have a joint distribution of x and y where • x has population mean ug and population variance o? • y has population mean ly and population variance o, and the population covariance between them is Ery. The population Pearson correlation is then given by Ery OxJy We collect n pairs of data, (X;, Yi), i = 1,.. , n. Each pair is an independent draw from this distribution. (a) Suppose we estimate our population covariance with n 1 (x; – Ha)(yi – µy). i=1 Is this an unbiased estimator of the population covariance? Show why or why not. (b) Suppose we estimate our correlation with (xi – Ha)(Yi – Hy) - n i=1 Ox0y Is this an unbiased estimator of the population correlation? Show why or why not. =WI
4) A set of measurements is given as follows. X = [0.1, 0.3, 0.8, 12,4, 7,9] We want to approximate the source of this data with Gamma distribution, i.e., X~Gamma(a, B). For Gamma distribution, the mean and variance can be found from the below equations. a Hx a o = Find the parameters of Gamma distribution to fit the data. Come up with two other distributions that you think are good representation of this data. Justify your answer.
Question 2. Let X be a normal random variable with u = -5 and o? = 4. a) Find P(X -3|X > -5).
Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean ? = 55.0 kg and standard deviation ? = 8.4 kg. Suppose a doe that weighs less than 46 kg is considered undernourished. (a) What is the probability that a single doe captured (weighed and released) at random in December is undernourished? (Round your answer to four decimal places.)(b) If the park has about 2850 does, what number do you expect to be undernourished in December? (Round your answer to the nearest whole number.)does(c) To estimate the health of the December doe population, park rangers use the rule that the average weight of n = 40 does should be more than 52 kg. If the average weight is less than 52 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weight x for a random sample of 40 does is less than…
Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean ? = 53.0 kg and standard deviation ? = 8.7 kg. Suppose a doe that weighs less than 44 kg is considered undernourished. (a) What is the probability that a single doe captured (weighed and released) at random in December is undernourished? (Round your answer to four decimal places.)(b) If the park has about 2150 does, what number do you expect to be undernourished in December? (Round your answer to the nearest whole number.)____ does(c) To estimate the health of the December doe population, park rangers use the rule that the average weight of n = 80 does should be more than 50 kg. If the average weight is less than 50 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weight x for a random sample of 80 does is less…
В2. (a) Given the probability Venn diagram below for the two Events A and B find the probabilities: 0.6 0.5 A 0.2 (i) (ii) (iii) Pr( A 'OR' B) Pr( Not-A 'AND' Not-B) Pr( Not-A "OR' Not-B) (b) A random sample from a population of X with unknown mean but a known variance, o = 400, gives the following data: sample size, n= 125, Ex= 1750. (i) Give a point estimate of the population mean, u. (ii) Is this estimate biased or not. Give a reason. (ii) Derive a 95% confidence interval for the population mean, µ.
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Can you help with part b without using Chebyshev's theorem
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