Discrete vs. Continuous RVs (Random Variables)

  • A discrete RV has a countable number of possible outcomes

    • number of students present

    • number of red marbles in a jar

    • number of heads when flipping three coins

    • students' grade level

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  • A continuous RV can take any values in an interval of numbers

    • height of students in class

    • weight of students in class

    • time it takes to get to school

    • distance traveled between classes

    P (a < X < b) = area of shaded region

Probability Distribution

  • The probability distribution of a discrete RV(X) list all the values possible and their probabilities

    List cf possible vdues Prob±iliy of each vaile x 1/4 1/2 1/4

  • The probabilities must:

    • All be a number between 0 and 1

    • Together add up to 1

Mean = Expected Value

  • Formula

    џх хи + хуг+ + хкрк 2х,в

  • Calculator

    • Type in X in L1 and P in L2

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  • 1-Var Stats L1, L2

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Variance = Standard Deviation

  • Formula


  • Calculator

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Practice Questions

  • A bin contains ten $1 bills, five $2 bills, three $5 bills, one $10 bill, and one $100 bill. A person is charged $10 to select one bill. Let the random variable (X) be the amount someone wins by playing.

    • Construct a probability distribution for these data.

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  • What is the mean and standard deviation of the amount of money someone can expect to win?


  • You work for a company and are tasked with evaluating a proposed venture. The venture stands to make a profit of $10,000 with probability 4/20, to make a profit of $5200 with probability 8/20, to break even with probability 1/4, and to lose $5000 with probability 3/20. The expected profit in dollars is? Would you recommend this venture?

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  • Answer: The expected profit is $3330. Recommend, because the standard deviation is not so large

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