In poisson distribution, how to find the mean and the variance?

Question

What is the difference between them?
what is the meaning of P(x>4 + var(x))?

Answer 1

p(x;λ)=(e^-λ) * (λ^x) / (x!)
with
Mean=λ (the expected value of probability)
Variance=λ (indicates dispersion)

P(x>4 + var(x)), is the probability that the random variable has of being greater than 4+var(x).

Answer 2

What Sparky says above has nothing to do with the Poisson distribution.
The Poisson distribution is a distribution of rare events happening over some time period (or flaws in a fixed area). The mean is found empirically by counting and averaging the number of events during a fixed time period (or fixed area). This number of events (or flaws) has no upper limit, and unlike the binomial distribution, the Poisson has no sample size. However, the Poisson can approximate the binomial when p is small and n is large. The advantage is that, because the Poisson has only one parameter, many probabilities are easily presented in table form.
The variance of the Poisson is the SAME as the mean and both are usually given the symbol, lambda.
Your expression makes little practical sense.

Answer 3

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Answer 4

The mean is the all the values (v) added ( summated) divided by the number of values (n)
V .......... n
5.1 ....... 5.1 2
5.4; 5.4; 5.4; 5.4 ..... 4 ....... ( 4 @5.4 see?)
5.6 ;.... 5.6 ...... 2
5.7 ; 5.7 ........ 2
total ........... ( number of items / observation)
54.4 ......... 10



Mean ..................... 54.4/10 = 5.44




The variance is how much the Value/ Observation / measurement (V) is away from the MEAN

Value ......... mean ........ Variance

5.1 ...... 5.44 ...... - 0.34
5.2 ...... 5.44 ...... - 0.24

5.6 ...... 5.44 ...... +.16