Assume that the number of network errors experienced in a dry on a local area ne

Question

Assume that the number of network errors experienced in a dry on a local area network (UNN) is distributed as a Poison validate. The mean number of network errors experienced in a day is 2.1. Complete parts (a) through (d) below. What is the probability that is any given dry zero network errors will occur? The probability that zero network errors will occur is (Round to four decimal places as needed.) What is the probability that is any given dry exactly one network error will occur? The probability that exactly one network error will occur is (Round to four decimal places as needed.) What is the probability that in any given dry two or more network errors will occur? (Round to four decimal places as needed.) The probability that two or more network error will occur is (Round to four decimal places as needed.) What is the probability that in any given dry fewer than three network errors will occur? (Round to four decimal places as needed.)

Explanation / Answer

Possion Distribution
PMF of P.D is = f ( k ) = e- x / x!
Where   
= parameter of the distribution.
x = is the number of independent trials
a.
P( X = 0 ) = e ^-2.1 * 2.1^0 / 0! = 0.1225
b.
P( X = 1 ) = e ^-2.1 * 2.1^1 / 1! = 0.2572
c.
P( X < 2) = P(X=1) + P(X=0)   
= e^-2.1 * 1 ^ 1 / 1! + e^-2.1 * ^ 0 / 0!
= 0.3796
P( X > = 2 ) = 1 - P (X < 2) = 0.6204
d.
P( X < 3) = P(X=2) + P(X=1) + P(X=0)
= e^-2.1 * 1 ^ 2 / 2! + e^-2.1 * ^ 1 / 1! + e^-2.1 * ^ 0 / 0!   
= 0.6496

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