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.
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!}
$
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 $\displaystyle E[X] = \lambda$.