Using Poisson random variables to calculate this probability

In summary, the conversation discusses the calculation of the mean and standard deviation, as well as a question regarding the probability of having fewer than 196 events in a given time period with a Poisson frequency of 2.5. The speaker also mentions their incorrect solution and asks for help on solving the question.
  • #1
Karl Porter
31
5
Homework Statement
A certain theory supposed that mistakes in cell division occur according to a Poisson process with rate 2.5 per year, an individual dies when 196 mistakes have occured.
Relevant Equations
c) the probability that an individual reaches age 90
d)find the probability that an individual died before age 67.2
I calculated the mean which is 78.4
And the Standard deviation is 5.6
I thought the answer would be (90^(-78.4)/78.4!)*e^-90
But looking back having a decimal factorial doesn't make sense

I have the numerical answers for c)= 0.019226
and d)=0.022750
but I my solution was wrong.

Any help on how this question is actually solved would be great
 
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  • #2
The clue that your answer is wrong lies in the fact that you haven't used the given number of 196, even though the answer must depend on that - the greater the number of mistakes needed to kill, the longer the expected life.
What is the probability of having fewer than 196 events in a time period of length 90, given a Poisson frequency of 2.5?
 

FAQ: Using Poisson random variables to calculate this probability

What is a Poisson random variable?

A Poisson random variable is a discrete random variable that represents the number of events that occur in a fixed interval of time or space, given that these events occur independently and at a constant rate.

How is a Poisson random variable used to calculate probability?

A Poisson random variable is used to calculate the probability of a certain number of events occurring in a given interval. This is done by using the Poisson probability formula, which takes into account the rate of occurrence and the number of events in the interval.

What is the difference between a Poisson random variable and a binomial random variable?

While both Poisson and binomial random variables are used to represent the number of events, the main difference is that a binomial random variable represents the number of successes in a fixed number of trials, while a Poisson random variable represents the number of events in a fixed interval of time or space.

Can a Poisson random variable be used for continuous data?

No, a Poisson random variable is used for discrete data, meaning that the events can only take on whole number values. It cannot be used for continuous data, which can take on any value within a range.

What are some real-world applications of using Poisson random variables to calculate probability?

Poisson random variables are commonly used in fields such as insurance, finance, and healthcare to model the occurrence of rare events. They are also used in traffic engineering to model the number of cars passing through a certain point in a given time interval.

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