**Theorem 1**: If the probability *p* of success of a single trial approaches 0 while the number of trials *n* approaches infinity and the value *μ = np* stays fixed, then the binomial distribution *B*(*n, p*) approaches the Poisson distribution with mean *μ*.

Proof: Let be the pdf for a binomial distribution as described in the statement of the theorem. Then

Thus as *p* → 0 and *n* → , with *μ = np* fixed, we have

which completes the proof.

good work. i would like to get these lecture notes for statistical analysis through my email.

thank you.

George,

Sorry, but I can’t make the lecture notes available via email. I plan to provide a book which contains these lecture notes which you can purchase for a modest fee, but the book is not yet available.

Charles