1.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 continuous random variable X with pdf of the form f(x) = { S(1 +x)°,x>0 a) Find the constant e? b) Find the cumulative distribution function of X? c) Find P(0.40s X s 0.45)?

1.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 continuous random variable X with pdf of the form f(x) = { S(1 +x)°,x>0 a) Find the constant e? b) Find the cumulative distribution function of X? c) Find P(0.40s X s 0.45)?

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

1. Let X be a Poisson random variable on the non-negative integers with rate λ = 4. Let W = 2X + 10. (a) What is the range of W? (b) Find a formula for Pw(k).
(24) Let X be a random variable with p.d.f. Ze-2 0
7. a) Suppose that X is a uniform continuous random variable where 0
Q1. let Y₁ < Y₂ < Y3 < Y4 < Y5 are the order statistics of the random sample of size 5 from the distribution : f(x) = 3x², 0
(50) Let X be a random variable with p.d.f. k 1
2. The random variable X is the amount of fructose in apples (in ounces) grown at a local orchard and is represented by the following cdf: 2(x +), 1
(a) Let Y be a random variable distributed as X. Determine E(Y) in terms of r. (b) Let {X1, X2, . .. , Xn} be a random sample drawn from a normal distirbution with mean u and 1 variance o?. Denote S E-(X; – X)² as the sample standard deviation. Use the 1 n - result in part (a), or otherwise, to find E(S). (c) Find an unbiased estimator for the population standard deviation o.
If Y = InX has a N (0, 1) distribution then E (X²) is equal to
Example 2.14. Show the CDF of the random variable X with the following pdf: fx(x) = l0.2(=)
5. Let X be a positive random variable; i.e., P(X - log(EX) (b) E[log(1/X)] > log[1/EX] (c) E (X³) > (EX)³
Chapters: Normal and Exponential random variables. Q: Let X be an exponential random variable with rate 1. If a and b are positive numbers, then P(X > a + b|X > b) = P(X > a). a. Explain why this is called the memoryless property b. Show that for an exponential rv X with rate 1, P(X > a) = e-ad.