Exponential Distribution

1
Exponential Distribution

• The RV T has an exponential distribution with
  rate l (for l gt 0) if T has the probability
  density
• The mean and standard deviation of T are

2
Exponential Distribution

• The exponential distribution is used to model
  waiting times for the occurrence of some event
  (death, failure, mutation, radioactive decay,
  etc.).
• The continuous analog of the geometric
  distribution.
• Models the successive inter-arrival times of a
  Poisson process in time.

3

• Suppose a particular kind of radioactive atom has
  a half-life of 2 years. Find
• The probability that an atom of this type
  survives at least 5 years.
• The time at which the expected number of atoms is
  10 of the original amount.

4
Gamma Distribution

• If Tr is the time of the rth arrival after t 0
  in a Poisson process with rate l, then Tr has the
  gamma (r, l) distribution with probability
  density
• The mean and standard deviation of Tr are