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Q. Illustrate Exponential Distribution?
Ans.
These are two examples of events that have an exponential distribution:
The length of time you wait at a bus stop for the next bus.
The length of time a scientist waits with a Geiger counter until a radioactive particle is recorded.
The exponential distribution occurs when events comply with the following requirements:
Requirements
Events occur randomly over time according to the following:
1. Independence - the number of occurrences in non-overlapping intervals are independent.
2. Individuality - events don't occur too close to each other (i.e. in a short amount of time the probability of 2 or more occurrences is zero.)
3. Uniformity - there is a constant rate at which occurrences occur.
If X represents the length of time we wait for the first occurrence, then X has an exponential distribution.
Ut=Uxx+A exp(-bx) u(x,0)=A/b^2(1-exp(-bx)) u(0,t)=0 u(1,t)=-A/b^2 exp(-b)
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Terminology of polynomial Next we need to get some terminology out of the way. Monomial polynomial A monomial is a polynomial which consists of exactly one term.
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Let's start things by searching for a mixing problem. Previously we saw these were back in the first order section. In those problems we had a tank of liquid with several kinds of
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