2. A printer ink cartridge has a life of X hours. The variable X is modeled by the probabil:S 400x-2x > 400density function f(x) =%3DotherwiseCalculatea) median lifetime of these cartridgesb) value of b such that P(X < b) = 0.6

For a continuous random variable, X, with probability density function fx, the probability that X…

Answered: 2. A printer ink cartridge has a life…

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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The lifetime, X, of a particular integrated circuit has an exponential distribution with rate of λ=0.5 per year. Thus, the density of X is: f(x,x) = 1 e-^x for 0 ≤ x ≤ ∞o, λ = 0.5. λ is what R calls rate. Hint: This is a problem involving the exponential distribution. Knowing the parameter for the distribution allows you to easily answer parts a,b,c and use the built-in R functions for the exponential distribution (dexp(), pexp(), qexp()) for other parts. Or (not recommended) you should be able to use the R integrate command with f(x) defined as above or with dexp() for all parts. d) What is the probability that X is greater than its expected value? e) What is the probability that X is > 5? f) What is the probability that X is> 10? g) What is the probability that X > 10 given that X > 5? h) What is the median of X? Please solution USING R script
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2. A printer ink cartridge has a life of X hours. The variable X is modeled by the probabi density function f(x) = 400x-2 x > 400 otherwise Calculate a) median lifetime of these cartridges b) value of b such that P(X < b) = 0.6