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 < 6 What is the cumulative distribution function, F(x)? What is the probability of a widget being made earlier than 4 s?

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 < 6 What is the cumulative distribution function, F(x)? What is the probability of a widget being made earlier than 4 s?

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 25EQ

See similar textbooks

Related questions

Q: After testing their AAA batteries, Duracell found that the lifetime of the batteries are…

Q: solve In random sampling from the exponential distribution, f(x) =1 θθe x− , x > 0, θ> 0, find the…

A: Given that The point mass function of X is f(x)=thetax(1-theta)1-x x=1 or 0 We have to find…

Q: 36. Assume that X is a continuous random variable with pdf f(x) = exp [-(x + 2)] if -2 <x< o and…

A: Moment Generating Function (m.g.f.): Let X be a random variable with probability function…

Q: In designing an electrical circuit, a probability density function is needed to b integrated to…

Q: The following table gives the total endothermic reactions involving sodium bicarbonate Final…

Q: For a certain insured, the distribution of aggregate claims is binomial with parameters m = 12 and q…

A: If X ~ B(n, p), then X has Binomial Distribution with parameters n and p, Then, E(X) = np

Q: Let the random variable X be the portion of a flood insurance claim for flooding damage to a house.…

A: The probability density of X has the form: f(x)= c(3x2 - 8x - 5) for 0 < x < 1 For a…

Q: (a) By a process of repeated sampling from a stationary population, the probability density function…

A: Given:-

Q: Q1: Let f(x) =2/x^3 ; 1<x<o, zero elsewhere Is p.d.f find 1- The cumulative distribution function…

A: Ans . f(x) = 2/x3 ; 1<x<infinite 1. CDF = P ( X<x ) = ∫1x2/x^3 dx = (…

Q: A researcher finds that the following pdf fits the daily returns for a portfolio manager, f(x|01,…

Q: 2) After testing their AAA batteries, Duracell found that the lifetime of the batteries are…

Q: Q3 Let X be a continuous random variable with PDF S 4x³ px(x) = 0 < x < 1 otherwise Find E(X) and…

Q: 6. Find the equation of the normal line to the graph of g(x) = v2-x at x= -7 %3D

A: Definition used - The slope of a normal line…

Q: The heat index (HI) is an estimate of the temperature felt by the human body based on the actual…

A: Answer is mentioned below

Q: 1. SupposeX1,..., Xniid∼Exponential(λ) is a set of n observations drawn independently from an…

A: We have given that, X1, X2, . . . . . . . . , Xn iid ~ Exp( λ ). The pdf of exponential…

Q: i) Find the cumulative distribution function (CDF) of X. 8 ii) Show that the moment generating…

Q: X follows a gamma distribution with PDF f(x) = 4xe-2x , where X > 0 (a) Derive E(Xn ).

A: Given, fx=4xe-2x, x>0 Therefore, Exn=∫0∞xnfxdx=∫0∞xn×4xe-2xdx=∫0∞4×xn+1e-2xdx=4×∫0∞xn+2-1e-2x dx

Q: 51. For which values of a does eax dx converge?

Q: Let X be the time in hours that the battery of a solar calculator functions properly between…

A: Given, Let X be the time in hours that the battery of a solar calculator functions properly between…

Q: a variance of 0.27. Test the company's claim at a = 0.05. n241

A: Given: The provided sample variance is s2 =0.27 and the sample size is given by n = 41. The…

Q: 6. Show that a gamma distribution with a> 1 has a relative maximum at x = (a- 1)B. What happens when…

A: We have to show that : gamma distribution with alpha >1 has a relative maximum at x=(alpha -…

Q: The time, X, to infection for Eagle Flu in minutes, after coming into contact with the virus has…

Q: 2. The time (in minutes) required for technicians to perform a specific task is believed to follow…

Q: A college professor never finishes his lecture before the end of the hour and always finishes his…

Q: 0, a) What is the marginal distribution of Z2. b) Find P(Z2 <)

A: here given joint probability density function of z1 and z2

Q: A room is equipped with four led light bulbs. The lighting system is programmed so that one led bulb…

A: From the given information, A room is equipped with four led light bulbs. The lifetime of each bulb…

Q: 2. A college professor never finishes his lecture before the end of the hour and always finishes his…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: 2. A college professor never finishes his lecture before the end of the hour and always finishes his…

A: ANSWER:-

Q: Suppose that X has a lognormal distribution with parameters 0 = 5 and w2 = 9. Determine the…

A: We have given that, Let X be the random variable from Log normal distribution with parameters θ = 5…

Q: The heat index (HI) is an estimate of the temperature felt by the human body based on the actual…

A: Given that, The heat index (HI) is an estimate of the temperature felt by the human body based on…

Q: Q2- Let random variable X has the following PDF 2х 0 < x < k f(x) = }k2 О.w find k such that Var(3X)…

A: Given: fx=2xk2 0<x<k0 otherwise Var (3X) = 2

Q: If the cumulative distribution [Q5B] function of f(x) is F(x), find: E(X) 1- e-8x x > 0 F(x) =…

A: Cumulative function of fx is given as follow: Fx:1-e-8x x≥00 otherwise We need to…

Q: A) | kx 0 1 B) Obtain the 25th percentile and the 75th percentile of the distribution.

Q: The temperature readings from a thermocouple in a furnace fluctuate according to a cumulative…

A: It is an important part of statistics. It is widely used.

Q: A model for lifetimes, with a bathtub-shaped hazard rate, is the ex- ponential power distribution…

Q: consecutive cars on a freeway during period of heavy flow (sec). Suppose that in a particular…

Q: Let X be the time in hours that the battery of a solar calculator functions properly between…

A: Since you have posted a question with multiple sub-parts, we have provided answer for first 3…

Q: A machine produces copper wire, and occasionally there is a flaw at some point along the wire. The…

Q: The time, X, to infection for Eagle Flu in minutes, after coming into contact with the virus has…

Q: • What is the probability that neither window is busy more than one-quarter of the time? • What is…

A: Here use given joint distribution of x and y

Q: Two components of a computer have the follow- ing joint pdf for their useful lifetimes X and Y:…

A: Given:

Q: mean(log X)= 3.4, Sjogx = 0.136 and k=1.2, using the log Pearson Type III distribution. The…

A: Option A

Q: Suppose the random variable T is the length of life of an object (possibly the lifetime of an…

Q: 11 dx Determine whether is convergent or not. (3 – x)2/3

A: As the value of Integral is finite, it converges.

Q: Suppose that the length X of the life (in years) of a battery for a computer has a distribution that…

Q: ge of X is {0, 1, 2, ...}. e non-integer answers in the form of proper fractions for the cumulative…

A: Giventhe cumulative distribution function for the random variable X with the probability mass…

Q: The time taken by a student to finish a statistics exam can be modeled using the following…

Q: The reaction time (in seconds) to a stimulus is a continuous random variable with pdf f(x) =…

Q: Suppose that each individual in a large insurance portfolio incurs losses according to an…

A: Given that each individual in a large insurance portfolio incurs losses according to an exponential…

Question

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 < 6

What 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

Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.

Expert Solution

Step 1

Given density function:

$f (x) = \frac{1}{162} {(x - 3)}^{2} (x + 6), 0 < x < 6$

Cumulative distribution function, F(X):

$F (x) = \int_{0}^{x} f (t) d t = \int_{0}^{x} \frac{1}{162} {(t - 3)}^{2} (t + 6) d t = \frac{x (x^{3} - 54 x + 216)}{648}$

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

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 .
Let X = the time between two successive arrivals at the drive-up window of a local bank. If X has an exponential distribution with λ = 1 Compute P(X≤4) and P(2≤X≤5)
A catalyst researcher states that the diameters, in microns, of the pores in a new product she has made have the exponential distribution with parameter λ = 0.25. Suppose that the diameters of 10 pores are independent. a) Find the probability that more than seven of them have diameters less than 3 microns. b) Find the probability that exactly one of them has a diameter greater than 11 microns.
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?
Workers at a large toxic cleanup project are concerned that their white blood cell counts may have been reduced. Let x be a random variable that represents white blood cell count per cubic millimeter of whole blood in a healthy adult. Then ? = 7500 and ? ≈ 1750.† A random sample of n = 50 workers from the toxic cleanup site were given a blood test that showed x = 6760. What is the probability that, for healthy adults, x will be this low or lower? (a) How does the central limit theorem apply? Explain. The central limit theorem describes the distribution of x as normal with mean ? x = 7500 and ? x ≈ 247.49.The central limit theorem describes the distribution of x as normal with mean ? x = 7500 and ? x ≈ 1750.00. The central limit theorem describes the distribution of x as normal with mean ? x = 7500 and ? x ≈ 35.00.The central limit theorem does not apply because the sample size is too small. (b) Compute P(x ≤ 6760). (Round your answer to four decimal places.) P(x ≤…