Data Science Classroom Series – 05/Dec/2021

Exponential Distribution

  • The time between events in Poisson process (i.e. inverse of Poisson) Preview
  • 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

Preview

  • 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 Preview
      • after 30 minutes Preview
      • 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 Preview
  • Chi-squared distribution is primarily used in hypothesis test for comparing Goodness of fit (theoreticial probabiliites vs Outcome Probabilities)
  • Expected Value and variance Preview
  • Visualization: Preview
  • TEST Statistic Preview
  • 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 Preview
    • 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

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