MDM4U – Grade 12 Data Management – Probability Distributions Test

Grade 12 – Data Management

Probability Distributions

Basic Probability Distributions

  • Random Variable: By letting X be a random variable, can generalize the probability to obtain the number times something happens
  • Probability Distributions can be created in a Table then graphed into a histogram to analyze the probability of each event happening
  • Expected Value: Expectation or expected value, E(X), is the predicted average of all possible outcomes of a probability experiment. In essence, it is a weighted mean of all the outcomes.

E(x) = Summation of (X*P(x)

  • X: Random variable value, P: Probability of the random variable


Binomial Distribution

  • All trials are independent
  • Only 2 possible outcomes (Success or failures)
  • Probability of success is the same on every level
  • Usually replaceable items
  • Binomial Distribution Formula
  • P(x) = (nCx) Px Qn-x
  • n: number of trials, P: probability, Q: 1-probability, X: random variable
  • Shortcut Expected Value Formula
  • E(x) = np
  • n: number of trials, P: probability


Hypergeometric Distributions

  • Hypergeometric Distributions are used for sampling without replacement.
  • Expected value of the sample should be proportional to the population
  • Outcomes are still 2 possibilities (Success or Failures)
  • Probabilities are not the same each time
  • Dependent Events
  • Not replaceable
  • Formula for Hypergeometric Distributions