The lifetime, in years, of a certain type of fuel cell is a random variable with probability density function k x>0 S(x) ={(x+3)* Using Determine the value k so that f(x) becomes a pdf. Using cumulative distribution function (CDF) method finds the probability that a fuel cell lasts more than 5 years? P(X>20 | X<40).

The lifetime, in years, of a certain type of fuel cell is a random variable with probability density function k x>0 S(x) ={(x+3)* Using Determine the value k so that f(x) becomes a pdf. Using cumulative distribution function (CDF) method finds the probability that a fuel cell lasts more than 5 years? P(X>20 | X<40).

Name: Solve All (3) parts The lifetime, in years, of a certain type of fuel
Uploaded: 2024-03-20T06:46:14.000Z
Channel: Bartleby
Description: Solve All (3) parts The lifetime, in years, of a certain type of fuel cell is a random variable with probabilitydensity functionkx>0S(x) = {(x+3)*UsingDetermine the value k so that f(x) becomes a pdf.Using cumulative distribution function (CDF) metho

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.6: Variation

Problem 2E

See similar textbooks

Similar questions

The time for the first widget to be manufactured each morning is random between 1 and 3 seconds with a pdf of f(x)=1/162(x-3)^2(x+6) for 0 < x < 6What is the cumulative distribution function, F(x)? What is the probability of a widget being made earlier than 4 s?Answer to four decimal places What is the probability of a widget being made later than 1.3 s?Answer to four decimal places
X1 and X2 are two discrete random variables, while the X1 random variable takes the values x1 = 1, x1 = 2 and x1 = 3, while the X2 random variable takes the values x2 = 10, x2 = 20 and x2 = 30. The combined probability mass function of the random variables X1 and X2 (pX1, X2 (x1, x2)) is given in the table below a) Find the marginal probability mass function (pX1 (X1)) of the random variable X1.b) Find the marginal probability mass function (pX2 (X2)) of the random variable X2.c) Find the expected value of the random variable X1.d) Find the expected value of the random variable X2.e) Find the variance of the random variable X1.f) Find the variance of the random variable X2.g) pX1 | X2 (x1 | x2 = 10) Find the mass function of the given conditional probability.h) pX2 | X1 (x2 | x1 = 2) Find the mass function of the given conditional probability.i) Are the random variables X1 and X2 independent? Show it. The combined probability mass function of the random variables X1 and X2 is below
Let the random variable X be the portion of a flood insurance claim for flooding damage to a house. The probability density of X has the form f(x)= c(3x2 - 8x - 5) for 0 < x < 1. What is the value of the constant c? What is the cumulative distribution function of X?
LetX1,X2,...,Xn be a sequence of independent and identically distributed random variables having the Exponential(λ) distribution,λ >0, fXi(x) ={λe−λx, x >0 0, otherwise (a) Show that the moment generating function mX(s) :=E(esX) =λ/(λ−s) for s< λ;
Suppose X1,...,Xn are measurements of the mass of an object. The measurements are normally distributed, with mean equal to mu , the mass of the object, and standard deviation equal to 1 microgram. Find (a) The likelihood function. (b) The log-likelihood function (c) the maximum likelihood estimator for the unknown parameter, and
Let X be a random variable with mean μ and variance _2. Show that E[(X − b)2], as a function of b, is minimized when b = μ.
A random variable X has cumulative distribution functionFX(t) ={0 t < 1 1/2t − 1/2 1 ≤ t < 2 1/2 2 ≤ t < 3 1/2t − 1 3 ≤ t < 4 1 4 ≤ t What is the range of X? Compute the probability that |X − 2.5| ≤ 1. Compute the PDF of X.
Find the maximum likelihood estimator for θ in the pdf f(y; θ) = 2y/(1 − θ^2), θ ≤ y ≤ 1.
The lifetime of a certain type of TV remote control is given by Y . Suppose Y has approximately exponential distribution with mean 8 years. a) Find the probability that a remote control of this type will last more than 15 years. b) Find the probability that of eight such remote controls at least one will last more than 15 years. c) What should the warranty period for these remote controls be if the manufacturer wants 85% of the remote controls to last beyond the warranty period? d) What is the moment generating function of Y .
If the PDF of X is f(x)=2x/k2 for 0<x<k, for what value of k is the variance of X equal to 2?
As baby boomers enter their golden years, the number of people afflicted with Alzheimer's disease is expected to rise dramatically. In a study published in the Journal of Neurology, the number of people with Alzheimer's disease in the United States age 65 years and over is projected to be N(t) = 0.00525t2 + 0.075t + 4.7 (0 ≤ t ≤ 4) million in decade t, where t = 0 corresponds to 2010.† (a)What is the projected number of people with Alzheimer's disease in the United States age 65 years and over in 2040? (Round your answer to four decimal places.) million (b) How fast is the number of people with Alzheimer's disease in the United States age 65 years and over projected to grow in 2040? million per decade (c)How fast is the rate of growth of people with Alzheimer's disease in the United States age 65 years and over projected to change in the period covered by the study? million per decade per decade
T has an exponential distribution such that P(T≤2)=2P(T>4) What is Var(T)=?