A machine produces copper wire, and occasionally there is a flaw at some point along the wire. Thelength of wire produced between successive flaws is a continuous random variable X with pdf of thec(1+x),x>0form f(x) =0.a) Find the constant c?b) Find the cumulative distribution function of X?c) Find P(0.40 X<0.45)?

Answered: Image /qna-images/answer/c1bd9cae-77b3-4731-825f-12ecc1599c83.jpg

A machine produces copper wire, and occasionally there is a flaw at some point along the wire. The length of wire produced between successive flaws is a contınuous random variable X with pdf of the Jel+x)³,x>0 form f(x) =- a) Find the constant c? b) Find the cumulative distribution function of X? c) Find P(0.40

A machine produces copper wire, and occasionally there is a flaw at some point along the wire. The length of wire produced between successive flaws is a contınuous random variable X with pdf of the Jel+x)³,x>0 form f(x) =- a) Find the constant c? b) Find the cumulative distribution function of X? c) Find P(0.40

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...

See similar textbooks

Similar questions

A random variable X has cumulative distribution functionFX(t) ={0 t < 11/2 t − 1/2 1 ≤ t < 21/2 2 ≤ t < 31/2 t − 1 3 ≤ t < 41 4 ≤ t What is the range of X? Compute the probability that |X − 2.5| ≤ 1. Compute the PDF 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;
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 Define the random variable Y=X1+X2+···+Xn. Find E(Y),Var(Y)and the moment generating function ofY.
Find the moment-generating function of the continuous random variable X whose probability density is given by f(x) = 1 for 0 < x < 1 0 elsewhere and use it to find μ’1,μ’2, and σ^2.
Use the moment generating function technique to solve. Let X1, . . . , Xn be independent random variables, such that Xi ∼ Exponential(θ), for i =1, . . . , n. Find the distribution of Y = X1 + · · · + Xn.
Consider a function F (x ) = 0, if x < 0 F (x ) = 1 − e^(−x) , if x ≥ 0 Is the corresponding random variable continuous?
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
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?
Consider X and Y are joint distributed with PDFf(x,y)=x+y, 0≤x≤1, 0≤y≤1. (a) Find the probability that X > 0.5. (b)FindP(X> Y 1/2).(c) Are X and Y independent?
The time, X, to infection for Eagle Flu in minutes, after coming into contact with the virus has cumulative distribution F with the following definition:F(x) = 0 for x < 1 and F(x)= (3/2)-(3/2x) for 0 ≤ x ≤ 3 a) What is the probability density function for X for 1 ≤ x ≤ 3? f(x) = .5 f(x) = (3/4x^2) f(x) =(3/2x^2) f(x) = (3/2)-(3/2x) f(x) = (3x/2x^3) b) What is the probability that X > 2? c) What is the probability X < 2 ? d) What is the probability that X > 2.5? e) What is the probability that X > 3? f) What is the probability that X > 2.5 given the X > 2? g) Calculate the 60th percentile of X. h) What is the expected value of X? i) What is the expected value of X2 j) What is the variance of X? k) What is the probability that X is more than 0.1 above its expected value?
Let f(x) = ½ , -1 < x < 1 0 otherwise be a pdf of the random variable X. Find the distribution function and the pdf of Y= X2