statistics 101 discrete and continuous random variables
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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