Answer:
The required answer is shown below:
Explanation:
Consider the provided information.
The formula for calculating poisson probability mass function:
Where λ is average number of events, the value of e = 2.718..
K can take the values 0,1,2...
Part (a)Find P(X = 7).
A certain mineral specimen is of such an age that there should be an average of 6 tracks per cm² of surface area.
Use the above formula and substitute x=7 and λ=6
Hence, P(X = 7) = 0.1377
Part (b)Find P(X ≥ 3).
This can be calculated as:
Hence, P(X ≥ 3) = 0.9380
Part (c)Find P(2 < X < 7).
The sum can be calculated as:
Hence, P(2 < X < 7)= 0.5443
Part (d)Find μX.
If λ is average number of successes or region in the Poisson distribution, then the mean and the variance of the Poisson distribution are both equal to λ.

Part (e)Find σX
If λ is average number of successes or region in the Poisson distribution, then the mean and the variance of the Poisson distribution are both equal to λ.


