The inter-arrival time X between faults in a network is exponential with parameter λ = 5.Hence, X has the pdf Jx(x)5e-5z0,I> 0x < 0.(a) Find the cdf Fx(x).(b) Find the probability that the inter-arrival time is at least 10.(c) Find E(X) (Use integration by parts).

Answered: Jx(x) = 5e-r 0. I≥0 I <0. (a) Find the…

Jx(x) = 5e-r 0. I≥0 I <0. (a) Find the cdf Fx(x). (b) Find the probability that the inter-arrival time is at least 10. (e) Find E(X) (Use integration by parts).

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter14: Discrete Dynamical Systems

Section14.3: Determining Stability

Problem 1YT

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Question

The inter-arrival time X between faults in a network is exponential with parameter λ = 5.
Hence, X has the pdf

Jx(x)
5e-5z
0,
I> 0
x < 0.
(a) Find the cdf Fx(x).
(b) Find the probability that the inter-arrival time is at least 10.
(c) Find E(X) (Use integration by parts).

Definition Definition Probability of occurrence of a continuous random variable within a specified range. When the value of a random variable, Y, is evaluated at a point Y=y, then the probability distribution function gives the probability that Y will take a value less than or equal to y. The probability distribution function formula for random Variable Y following the normal distribution is: F(y) = P (Y ≤ y) The value of probability distribution function for random variable lies between 0 and 1.

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