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140 Terms
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Formula of Mean
Σ(X) \= Σ[X·P(X)]
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Mean
expected value
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Mean
a parameter that measures the central location of the distribution of a random variable
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Mean
the long-run average value that would result from repeatedly running the experiment
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Mean
can be used to get an overall idea or picture of the data set
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1.) Construct the probability distribution.
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2.) Determine the value of X·P(X)
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3.) Add all the values of X·P(X)
Steps in Computing for the Mean of a Discrete Random Variable
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Mu Symbol
Name the Symbol
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µ
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Lowercase Sigma Symbol
Name the Symbol
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σ
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Uppercase Sigma Symbol
Name the Symbol
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Σ
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Variance
σ^2
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Standard Deviation
σ
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Variance and Standard Deviation
describes the dispersion or the variability of the distribution
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Formula of Variance
σ^2 \= Σ[X^2 · P(X)] - µ^2
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Formula of Standard Deviation
σ \= √Σ[X^2 · P(X)] - µ^2
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All values are identical
A variance of 0 indicates what?
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The data points are very spread out around the mean and from each other
What does a high variance indicate?
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The data points tend to be very close to the mean and to each other
What does a low variance indicate?
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Probability Distribution of a Discrete Random Variable
is a list
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Likelihood and Spread
a Probability Distribution of a Discrete Random Variable is useful in navigating these two categories
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Probability Mass Function
another term for Probability Distribution Function
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True
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31
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f(x)\=P(X\=x)
True or False: Properties of a Probability Mass Function
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The probabilities represents the function
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False
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The lower range is 0 and the upper boundary is 1.
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0 ≤ f(x) ≤ 1
True or False: Properties of a Probability Mass Function
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The probability of each outcome is between 0 and 1
inclusive.
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The lower range is 1 and the upper boundary is 0.
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True
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1 or 100%
True or False: Properties of a Probability Mass Function
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The sum of all the probabilities of the random variable is equal to 1.
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1. f(x)\=P(X\=x) (The probabilities represents the function)
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2. 0 ≤ f(x) ≤ 1 (The probability of each outcome is between 0 and 1
inclusive. The lower of range is 0 and the upper boundary is 1.
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3. The sum of all the probabilities of the random variable is equal to 1 or 100%.
Properties that must be satisfied in constructing a probability distribution
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Histogram
a graph of a probability mass function
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Possible Values of the Discrete Random Variable
these are what lies in the horizontal axis of a histogram
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Probabilities
these are what lies on the vertical axis of a histogram
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What the data represents
the horizontal axis of a histogram is labeled with
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Frequency or Relative Frequency
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Percent Frequency or Probability
the vertical axis of a histogram is labeled as
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Normal Distribution
a continuous probability distribution where most of the scores tend to be closer to the mean
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Normal Random Variable
a continuous random variable of a normal distribution
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Normal Curve
represents a normal distribution
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Spreadness
what does standard deviation determine in a distribution
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Standard Normal Distribution
the most common example of a normal distribution with a mean of 0 and a standard deviation of 1
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N(0
1)
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Normal
refers to the fact that this kind of distribution occurs in many different kinds of common measurements
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Normal Curve
a bell-shaped graph that represents a normal distribution
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Standard Deviation
is a measure of how dispersed the data is in relation to the mean
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False
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A normal distribution is SYMMETRIC about its mean.
True or False: Characteristics of a Normal Distribution
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A normal distribution is VARYING about its mean.
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True
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The mean
median
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The mean
median
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False
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A normal distribution is THICKER at the center and LESS THICK at the tails.
True or False: Characteristics of a Normal Distribution
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A normal distribution is LESS THICK at the center and THICKER at the tails.
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True
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Approximately 68.26% of the area of a normal distribution is within ONE standard deviation of the mean.
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p (µ - σ < X < µ + σ ) \= 0.6826
True or False: Characteristics of a Normal Distribution
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Approximately 68.26% of the area of a normal distribution is within ONE standard deviation of the mean.
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False
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Approximately 95.44% of the area of a normal distribution is within TWO standard deviations of the mean.
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p (µ - 2σ < X < µ + 2σ ) \= 0.9544
True or False: Characteristics of a Normal Distribution
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Approximately 95.44% of the area of a normal distribution is within THREE standard deviations of the mean.
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True
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Approximately 99.74% of the area of a normal distribution is within THREE standard deviations of the mean.
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p (µ - 3σ < X < µ + 3σ ) \= 0.9974
True or False: Characteristics of a Normal Distribution
Note 
Flashcards (58)