Exponential Distribution

• The time between events in Poisson process (i.e. inverse of Poisson)
• Poisson: Events per single unit of time
• Exponential: Time per single events
• Pre-req’s:
  • Events must occur at constant rate
  • Events must be independent of each other
• Exponential is a continuous distribution as it measure time which can be fractioned or divided
• Since it is continuous distribution, we will have probability distribution function(pdf)
• In Poisson distribution

mean = λ

• In exponential distribution

mean = μ = 1/λ

• Example:
  • Unique visitors arrive at the quality thought recpetion by a Poisson process at an average of 3 per hour.
  • Find the probability that the next visitor arrives
    • with in 10 minutes
    • after 30 minutes
    • in exactly 25 minutes => 0
• Excel Sheet
  • EXPON.DIST(x,lambda,cumulative)

CHI-Squared distribution -> 𝛘2 distibution

• IF Z1,Z2……Zk are the independent samples from standard Normal distribution
• Chi-squared distribution is primarily used in hypothesis test for comparing Goodness of fit (theoreticial probabiliites vs Outcome Probabilities)
• Expected Value and variance
• Visualization:
• TEST Statistic
• Example:
  • In an engineering class of 75 students, 11 are left-handed. Does this class fit the prevailing theory that 12% of the people are left handed
  • CONCLUSION:
    • There is not enough evidence to suggest the proportion of left handedness is other than 0.12
  • A poker dealing machine is supposed to deal cards at random from an infinite deck
    • In a test, you counted 1600 cards and observed the following
      • Spades: 404
      • Hearts: 420
      • Diamonds: 400
      • Clubs: 376
    • Is is set equally likely
• Refer Here for the excel sheet containing chi-squared tests