After 3 years of field research you have finally the manuscript of a standard work about the mating rivals of the hungarian horntail finished and now you want it to be proofreaded.

Let the amount of typing error be poisson-distributet with parameter λ > 0. Independently of each other you find each typing error with a probability of p ∈ (0,1) or you overlook it with a probability of 1- p.

1- Show that the amount of the found typing error and the amount of the overlooked ones are stochastically independend.

2- Calculate also the distribution.