Find the probabilities of events

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Reference no: EM13246928

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 23^o 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).

Reference no: EM13246928

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