section 7.1 discrete and continuous random variables
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Section 7.1 Discrete and Continuous Random Variables. AP Statistics. Random Variables. A random variable is a variable whose value is a numerical outcome of a random phenomenon. For example: Flip three coins and let X represent the number of heads. X is a random variable. - PowerPoint PPT PresentationTRANSCRIPT
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Section 7.1Discrete and Continuous Random VariablesAP Statistics
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AP Statistics, Section 7.1, Part 1 2
Random Variables
A random variable is a variable whose value is a numerical outcome of a random phenomenon.
For example: Flip three coins and let X represent the number of heads. X is a random variable.
We usually use capital letters to denotes random variables.
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AP Statistics, Section 7.1, Part 1 3
Random Variables
A random variable is a variable whose value is a numerical outcome of a random phenomenon.
For example: Flip three coins and let X represent the number of heads. X is a random variable.
The sample space S lists the possible values of the random variable X
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AP Statistics, Section 7.1, Part 1 4
Discrete Random Variable
A discrete random variable X has a countable number of possible values.
For example: Flip three coins and let X represent the number of heads. X is a discrete random variable.
We can use a table to show the probability distribution of a discrete random variable.
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AP Statistics, Section 7.1, Part 1 5
Discrete Probability Distribution Table
Value of X: x1 x2 x3 … xn
Probability:p1 p2 p3 … pn
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AP Statistics, Section 7.1, Part 1 6
Probability Distribution Table: Number of Heads Flipping 4 Coins
TTTT
TTTHTTHTTHTTHTTT
TTHHTHTHHTTHHTHTTHHTHHTT
THHHHTHHHHTHHHHT
HHHH
X 0 1 2 3 4
P(X) 1/16 4/16 6/16 4/16 1/16
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AP Statistics, Section 7.1, Part 1 7
Discrete Probability Distributions Can also be shown using a histogram
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AP Statistics, Section 7.1, Part 1 8
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AP Statistics, Section 7.1, Part 1 9
What is the average number of heads?
61 4 4 116 16 16 16 16
0 4 12 12 416 16 16 16 16
3216
0 1 2 3 4
2
x
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AP Statistics, Section 7.1, Part 1 10
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AP Statistics, Section 7.1, Part 1 11
Continuous Random Variable
A continuous random variable X takes all values in an interval of numbers.
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AP Statistics, Section 7.1, Part 1 12
Distribution of Continuous Random Variable
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AP Statistics, Section 7.1, Part 1 13
Distribution of Continuous Random Variable The probability distribution of X is
described by a density curve. The probability of any event is the area
under the density curve and above the values of X that make up that event.
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AP Statistics, Section 7.1, Part 1 14
Normal distributions as probability distributions Suppose X has N(μ,σ) then we can use
our tools to calculate probabilities.