Let X be a random variable denoting the number of -particles arriving independen
ID: 3232316 • Letter: L
Question
Let X be a random variable denoting the number of -particles arriving independently at a detector at the average rate of 0.1 per second. X can be modeled as Poisson(0.1) random variable. Let Y be the number of -particles detected during a one-minute interval. A) Specify the probability model for Y. B) Find P[Y>Y] C) The detector is turned on, and runs for one hour. If we view this hour as 60 one-minute intervals (nonoverlapping), what is the probability that during at least one of these 60 one-minute intervals, no particles are detected?
Explanation / Answer
Given mean = T = 0.1
Total time Y = 1 min = 60 sec
probability model for Y
mean = T * 60 = 6
poisson
= e^(-T)*T^x/x!
b) p(X>UY)
= p(X>6)
= 1 - p(X<=6)
= 1 - 0.285
= 0.715
c)
In the interval of 60 min
p(X=0)
= e^(-0.1*60*60)
= e^(-36)
= 2.13* 10^(-16)
x y 0 0.002479 1 0.014873 2 0.044618 3 0.089235 4 0.133853 5 0.160623 6 0.160623 7 0.137677 8 0.103258 9 0.068838 10 0.041303 11 0.022529 12 0.011264 13 0.005199 14 0.002228 15 0.000891 16 0.000334 17 0.000118 18 3.93E-05 19 1.24E-05 20 3.73E-06Related Questions
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