Statistics 101 Discrete and Continuous Random Variables.

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Statistics 101 Discrete and Continuous Random Variables

Transcript of Statistics 101 Discrete and Continuous Random Variables.

Page 1: Statistics 101 Discrete and Continuous Random Variables.

Statistics 101

Discrete and Continuous Random Variables

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Discrete Random Variable

Has a countable number of possible values

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Getting Good Grades

An instructor of a large college course gives 15% of each A’s and D’s, 30% each B’s and C’s and 10% F’s. Student’s are grades on a four-point scale (A = 4).

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Distribution of X:

Grade 0 1 2 3 4

Probability 0.10 0.15 0.30 0.30 0.15

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Question

What is the probability that the student earned a B or better?

Is this the sum of an A and a B?

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Answer

P(grade is 3 or 4)= P(3) + P(4) = 0.30 + 0.15 = 0.45

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Probability histograms for (a) random digits and (b) Benford’s law

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Example 7.2

Tossing Coins Assumptions

Balanced coin (Eric) Coin has no memory

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X is the number of heads

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Questions

P(X=2) = (number of ways X=2)/16 = 6/16

P(X=0) P(X=1) P(X=3) P(X=4)

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P(X=0) = 1/16 = 0.0625 P(X=1) = 4/16 = 0.25 P(X=3) = 4/16 = 0.25 P(X=4) = 1/16 = 0.0625

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Continuous random variables

Takes all values in an interval of numbers

Probability distribution – Described by a density curve

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Random numbers and the uniform distribution (Ex:7.3 pg. 398)

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Example 7.4 Drugs in Schools

1500 American Adults SRS N(0.3, 0.0118) What is the probability that the poll

differs from the truth about the population by more than two percentage points?

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Z-score

XZ

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Read Example p 401

Exercises 2, 4, 6, 8, 10, 15, 16, 19