A study conducted at Duke University in the mid 1990's (Madan Paidhungat, Dept of Molecular Cancer Biology) investigated the cell growth with two types of yeast cell genes: wild and mutant cdc-1. It was postulated that the mutant gene inhibits the cell growth.
Using the results of a large experimental study researchers modeled the wild and mutant cell growth (measured by a number of isolated colonies as X1 and X2 respectively) under 23o Celsius temperature and controlled environment (carbon source, richness and composition of media).
The postulated distributions were X1 ∼ Poi(64) for the wild cells and X2 ∼ Poi(55) for the cdc-1 mutants.
(a) Find the probabilities of events {X1 ≤ 60} or {X2 ≥ 60}.
(b) Find x* so that the probability of {X1 > x*} is 0.25.
(c) Take two independent counts X1 and X2 from their respective distributions and find the probability that X1 + X2 exceeds 100. Hint: If X1 ∼ Poi(λ1) and X2 ∼ Poi(λ2) are independent, then X1 + X2 ∼ Poi(λ1 + λ2).