The number of monthly breakdowns of a super computer is a random variable having a Poisson distribution with $\lambda=1.8$. Use the formula for the Poisson distribution to find the probabilities that this computer will function (a) without a breakdown; (b) with only one breakdown.
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Jason G.
5. The monthly breakdowns of a computer is a random variable having a Poisson distribution with mean equal to 1.8. Find the probability that this computer will function for a month without a breakdown.
Adi S.
Suppose events occur according to a Poisson process with rate $\lambda .$ (a) Given that $n$ events have occurred in the interval $[0, n],$ what is probability that $x$ of these events occurred in $[0,1] ?[$ Hint: Let $X(t)$ be the Poisson process, and write the conditional probability of interest in terms of $X(t) .$ Then apply the definition of conditional probability. (b) Given that $n$ events have occurred in the interval $[0, n],$ what is the limiting conditional distribution of the number of events in $[0,1]$ as $n \rightarrow \infty ?$
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