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Continuous distributions


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Continuous distributions

  1. 1. Continuous Distributions Uniform distribution. Exponential distribution. By one convention, a random variable X is called continuous if its cumulative distribution function is continuous. Ex. Shashwat Shriparv InfinitySoft
  2. 2. Uniform distribution …..  A random variable X is uniformly distributed on the interval interval (a,b) if its pdf is given by  The cdf is
  3. 3. pdf and cdf of Uniform distribution Probability density function Cumulative distribution function
  4. 4.  E(X)=(a+b)/2  V(X)=(b-a)2/12
  5. 5. Example  A bus arrives every 20 miutes at a specified stop beginning at 6:40 AM and continuing until 8:40 am. A certain passenger does not know the schedule, but arrives randomly (uniformly distributed) between 7:00 am and 7:30 am every morning. What is the probability that the passenger waits more than minutes for a bus?
  6. 6. Exponential distribution  A random variable X is said to be exponentially distributed with parameter λ > 0 if its pdf is given by
  7. 7. Probability density function
  8. 8. Cumulative distribution function
  9. 9. Exponential distribution ….
  10. 10. Example  suppose that the life of an industrial lamp, in thousands of hours , it exponentially distributed with failure rate λ=1/3 (one of failure every 3000 hours, on average).. The probability that the lamp will last longer than its mean life of giving 3000 hours is given by P(X>3)=1-P(X<=3) = 1-F(3)  P(X>3)=1-(1-e-3/3)=e-1 =0.368 Shashwat Shriparv InfinitySoft