Question

A computer network experiences attacks according to a Poisson process, at an average rate of 0.5 attacks per week. Let the random variable X measure the number of weeks until the network experiences its first attack. What is the probability the first attack will occur after the second week. That is to say, what is P(X 2) Round your answer to four decimal places. Answer: Save response

Answer 1

Solution :

Given that ,

mean = $\mu$ =

Using poisson probability formula,

P(X = x) = (e^-$\mu$ * $\mu$ ^x ) / x!

P(X $\geq$ 2) = 1 - P(X < 2 )

= 1 - (P(X = 0) + P(X = 1))

P(X = ) = 1 - ((e^-0.5 * 0.5⁰⁾ / 0! + (e^-0.5 * 0.5¹⁾ /1!)

= 1 - ( 0.6065 + 0.3033 )

= 1 - 0.9098

Probability = 0.0902