(Answered) A total of m cells are exposed to x-ray radiation x-rays

Statistics

A total of M cells are exposed to X-ray radiation. X-rays produce chromosome breakages in cells. For each individual cell i Є {1, .. . , M}, the number N2 of breakages has a Poisson distribution with parameter A (the random variables N are independent). Each breakage has a probability q of healing perfectly, a probability p of healing with a mutation, and a probability r = 1 - p - q of not healing (the associated events are independent between breakages). If all the breakages of a cell are not healed perfectly or healed with a mutation then the cell dies.

a) What is the probability that a given cell dies from the radiation?

b) What is the probability that a given cell survives the radiation without any mutations?

c) What is the probability that a given cell survives the radiation with at least one mutation?

d) What is the average number of mutations per surviving cells?

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