2. The consumer taste evaluation of a certain microwave dinner (on a continuous scale 0-10)X has cumulative distribution function F(x) = P(X ≤ x) = 120 (2 + x).a) Find the probability that the next consumer will evaluate the dinner as higher than a 5 butno higher than an 8.b) Calculate the expected value and variance of consumer evaluations.

(a) The probability that the next consumer will evaluate the dinner between 5 and 8 is 0.375 (or…

Answered: 2. The consumer taste evaluation of a…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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12. i. State Central limit theorem and tell what is the main theme of it. ii. Show that if the random variables (X, Y) follow the probability density of a bivariate normal distribution and if the correlation p = 0, X and Y are independent. (Show that f(x, y) = g(x) h(y))
Let X be a random variable that represents the level of glucose in the blood (milligrams per deciliter of blood). The distribution of X for a healthy person is normally distributed with men u = 85 and standard deviation o = 25. A person suffers from severe excess in insulin would have a lower level of glucose. A blood test with result of X < 40 would be used as an indicator that medication is needed. (a) What is the probability that a healthy person will be suggested with medication after a single test? (b) A doctor uses the average result of 2 tests for diagnosis, that is X. The second test will be conducted one week after the first test, so that the two test results are independent. For many healthy persons, each has finished two tests, find the expectation and standard error of the distribution of X. (c) The doctor suggests medication will be given only when the average level of glucoses in the 2 blood tests is less than 40, that is X < 40, so to reduce the chance of…
Show all work. Do not reuse a former solution.
Q4. Assume that daily evaporation rates (E) have a uniform distribution with a = 0 and b = 0.35 in/day. Determine the following probabilities: (a) P(E > 0.1); (b) P(E < 0.22); and (c) P(E = 0.2).
A random variable Z is normally distributed with mean and variance are 0 and 1 respectively. Determine the probability of P(√2 ≤ Z < √5)
Please answer exercise 2
Julia is currently age 30. She purchases a whole life insurance policy that pays a benefit of $1 at the moment of death. Let i = 0.06 In addition, suppose that Julia's mortality or age- at-failure (X) follows the Uniform Distribution on [0, 100]. Let Z be the present value random variable for the unit of payment made at the time point of failure. Calculate the expected value and variance of the present value of her death benefit.
The Weibull distribution is widely used in statistical problems relating to aging of solid insulating materials subjected to aging and stress. Use this distribution as a model for time (in hours) to failure of solid insulating specimens subjected to AC voltage. The values of the parameters depend on the voltage and temperature; suppose a = 2.4 and ß = 220. (a) What is the probability that a specimen's lifetime is at most 250? Less than 250? More than 300? (Round your answers to five decimal places.) at most 250 less than 250 more than 300 0.74310 0.74310 0.12183 (b) What is the probability that a specimen's lifetime is between 100 and 250? (Round your answer to four decimal places.) 6032 (c) What value (in hr) is such that exactly 50% of all specimens have lifetimes exceeding that value? (Round your answer to three decimal places.) hr

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