ФЫ В А ПРО В А П Р О Л ДЗАПРОЛДЖЭЯЧСМИТНЧСМИТЬБНСМИТЬБюSOLVE STEP BY STEP IN DIGITAL FORMAT11. The future lifetimes (in months) of two machine components have the following joint density function:6fxy(x,y) =(50-x-y), 0

Given the future lifetimes of two machine components have the following joint density function:We…

Answered: 11. The future lifetimes (in months) of…

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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A CI is desired for the true average stray-load loss μ (watts) for a certain type of induction motor when the line current is held at 10 amps for a speed of 1500 rpm. Assume that stray-load loss is normally distributed with = 2.1. (Round your answers to two decimal places.) (a) Compute a 95% CI for μ when n = 25 and x = 56.0. watts (b) Compute a 95% CI for μ when n = 100 and x = 56.0. watts (c) Compute a 99% CI for μ when n = 100 and x = 56.0. watts (d) Compute an 82% CI for μ when n = 100 and x = 56.0. watts (e) How large must n be if the width of the 99% interval for u is to be 1.0? (Round your answer up to the nearest whole number.) n =
1. Supercavitation is a propulsion technology for undersea vehicles that can greatly increase their speed. It occurs above approximately 50 meters per second when pressure drops sufficiently to allow the water to dissociate into water vapor, forming a gas bubble behind the vehicle. When the gas bubble completely encloses the vehicle, supercavitation is said to occur. Eight tests were conducted on a scale model of an undersea vehicle in a towing basin with the average observed speed x = 102.2 meters per second. Assume that speed is normally distributed with known standard deviation o =4 meters per second. 1.1. Test the hypothesis H0 : µ=100 versus H1: µ < 100 using a=0.05. 1.2. What is the P-value for the test in part 1.1.? 1.3. Compute the type II error if the true mean speed is as low as 95 meters per second. 1.4. What sample size would be required to detect a true mean speed as low as 95 meters per second if you are willing to accept a type Il error of 0.15?
A9. If the total benefit function is B = 192M – 4M^2, the total damage function is D = A2, ⍺ = 0.5 and there is no discounting where: M is the level of emissions. A is the stock of the pollutant. ⍺ is the linear decay rate of A a) What are the steady-state levels of M and A? b) Assuming now that we have some discounting and r = 0.2, where r is the social consumption discount rate. What are the new steady state levels of M and A?
2. In probability, it is common to model the deviation of a day's temperature from the monthly average temperature using the Gaussian probability density function, 1.-/9 f(t) = V9T This means that the probability that the day's temperature will be between t = a and t = b different from the monthly average temperature is given by the area under the graph of y = f(t) between t a andt = b. A related function is %3D F(x) = -2/9 dt, 2 0. %3D V9n Jo This function gives the probability that the day's temperature is between t = -x and t = x different from the monthly average temperature. For example, F(1) 0.36 indicates that there's roughly a 36% chance that the day's temperature will be within 1 degree (between 1 degree less and 1 degree more) of the monthly average. 1 (a) Find a power series representation of F(x) (write down the power series using sigma notation). (b) Use your answer to (a) to find a series equal to the probability that the day's temperature will be within 2 degrees of the…
2. An investor's losses follow a distribution with density function, f(x) =, x > 1 and 0 everywhere else, To recover her losses, the investor purchases an insurance policy with a deductible of $1. Show that the insurance company will go bankrupt. Hint: The expected amount of the losses paid by the company is too large.
Question content area top Part 1 A New York Times article reported that a survey conducted in 2014 included 36,000 adults, with 3.71% of them being regular users of e-cigarettes. Because e-cigarette use is relatively new, there is a need to obtain today's usage rate. How many adults must be surveyed now if a confidence level of 99% and a margin of error of 1.5 percentage points are wanted? Complete parts (a) through (c) below. Question content area bottom Part 1 a. Assume that nothing is known about the rate of e-cigarette usage among adults. n=. 015.015 (Round up to the nearest integer.)
A problem that occurs with certain types of mining is that some byproducts tend to be mildlyradioactive, and these products sometimes get into our freshwater supply. The EPA has issuedregulations concerning a limit on the amount of radioactivity in supplies of drinking water.Particularly, the maximum level for naturally occurring radiation is 5 picocuries per liter ofwater (on average). A random sample of 24 water specimens from a city’s water supply gave ̄x= 4.61 and s = 0.87. Do these data provide sufficient evidence to indicate that the meanlevel of radiation is safe (below the maximum level set by the EPA)? Test usingα= 0.05.

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11. The future lifetimes (in months) of two machine components have the following joint density function: 6 fxy (x, y) (50-x-y), 0