# 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