If the number of accidents occuring in an industrial plant during aa day is given by a Poisson random variable with parameter 3.

Find

i) probability that no accident occurs on a day

ii)the expected number of accidents per day.

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- Jan 6th 2009, 11:16 PMzorroPoisson Problem
If the number of accidents occuring in an industrial plant during aa day is given by a Poisson random variable with parameter 3.

Find

i) probability that no accident occurs on a day

ii)the expected number of accidents per day. - Jan 7th 2009, 05:53 AMmr fantastic
- Jan 7th 2009, 09:31 PMzorroThen is this right
probability of an accident happening in a day is

$\displaystyle

p(x;\lambda) \ = \ \frac{\lambda^x \ e^{- \lambda}}{x!} \ = \ \frac{3^x \ e^{-3}}{x!} = \frac{3^x \ 0.050}{x!}

$

probability of accident happening is

$\displaystyle

\left ( 1 - \frac{3^x \ 0.050}{x!} \right)

$

Expected no. of accidents per day is

$\displaystyle

E(X) = \sum x . p(x;\lambda) = \sum x \ . \ \frac{3^x \ . \ 0.050}{x!}

$ - Jan 7th 2009, 10:51 PMmr fantastic
- Jan 8th 2009, 12:04 AMzorrohw did u get E[x]
- Jan 8th 2009, 01:29 AMmr fantastic
No.

$\displaystyle E[X] = \sum x \cdot p(x; \, \lambda)$.

And the result of this calculation (which can be used without proof I would have thought unless the calculation is specifically asked for: http://www.mathhelpforum.com/math-he...tributiom.html) is $\displaystyle E[X] = \lambda$.