SOLUTION: Given that x has a Poisson distribution with mu equals 9, what is the probability that x equals 3?
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Question 1140089: Given that x has a Poisson distribution with mu equals 9, what is the probability that x equals 3?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the poisson probability formula is:
p(x) = m^x * e^(-m) / x!
m is the mean
x is the desired number that you want the probability for.
e is the scientific constant equal to 2.718281828.....
when m = 9 and x = 3,the formula becomes;
p(3) = 9^3 * e^(-9) / 3! = .01499 rounded to 4 decimal digits.
there is an online calculator that does the dirty work for you.
in addition, that calculator gives you much more than just the probability of exactly x occurrences.
that calculator can be found at https://www.algebra.com/tutors/faq.mpl
here's a display of the results from that calculator dealing with your problem.
here's a reference that tells you what the poisson probability distribution is and how to work with it.
https://stattrek.com/probability-distributions/poisson.aspx
note that the formula, shown as:
p(x) = m^x * e^(-m) / x!
m is the mean
x is the desired number that you want the probability for.
e is the scientific constant equal to 2.718281828.....
can also be shown as:
p(x) = m^x / (e^m * x!)
that's because e^(-m) is the same as 1 / e^m.
note that the calculator not only gives you p(x = 3).
it also gives you p(x < 3), p(x <= 3), p(x > 3), p(x >= 3).
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