2. A system consisting of one original unit plus a spare can function for arandom amount of time X. If the density function is given (units in months)byf(x) = {kxe x> 0.(a) What is the probability that the system functions for at most 4 months?(b) What is the probability that the system functions for at least 3 months?

Answered: Image /qna-images/answer/1092d424-0e13-4c32-8445-4026b97dcdde.jpg

Answered: 2. A system consisting of one original…

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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While taking a walk along the road where you live, you accidentally drop your glove, but you don't know where. The probability density p(x) for having dropped the glove a kilometers from home (along the road) is p(x) = 2e-2 for x ≥ 0 a. What is the probability that you dropped it within 1 kilometer of home? I b. At what distance y from home is the probability that you dropped it within y km of home equal to 0.95? km <-|
I want solutions of all these examples.
A company uses wood chips in the manufacture of processed wood pieces of various sizes. Suppose the tons of wood chips T used per day has a probability density function f(T) = 0.25e-0.25T (a) Find the probability of using more than 4 tons of wood chips in a day. (Round your answer to three decimal places.) (b) Find the number of tons 7 (to the nearest ton) so that the probability of using more than 7 tons in a day is 0.07. tons
7. Radar returns (power) are modeled in terms of the following (gamma) density, x X f(x) = ² ² e ²³ U (x) B (a) What is the value of B so that f(x) is a valid pdf? (b) What is the probability that the received power exceeds 2 units. (c) What is the probability that the received power is less tha 6 units. (d) What is the probability that the received power lies between 2 and 6 units (e) What is the probability that the received power is exactly 5 units. (f) If past observations have shown that the received power is always more than 3 units, what is the probability that the the received power will be less than 6 units. (g) What is theprobability that X²>4? (h) What is the probability that sqrt(X)>2?

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