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14 Cards in this Set
- Front
- Back
- 3rd side (hint)
Probability Distribution (of a discrete random variable)
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A list of probabilities associated with each of its possible values. The probabilities must satisfy the two requirements: Every probability is between 0 and 1 and the sum of the probabilities must equal 1.
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Discrete Random Variable
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A random variable, X, has a countable number of possible values.
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Random Variable
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A variable whose value is a numerical outcome of a random phenomenon
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Example:
When tossing a coin and if X is the number of heads, than X is a random variable because its values vary when the coin tossing is repeated. |
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Continuous Random Variable
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A variable that takes all values in an interval of numbers. Its probability distribution can be described with a density curve. Probability for a certain interval can be found by taking the area of the space between two values in its density curve. The probability of an individual outcome is 0.
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Example:
When observing the amount of rain falling in a city and X is rain in inches, X is a continuous random variable because there are infinite numbers of values. |
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Normal Distribution
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One type of continuous distribution. The normal distribution has a mean of 0 and standard deviation of 1.
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The bell curve histogram.
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Mean of Any Discrete Random Variable
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It is an average of the possible outcomes but a weighted average in which each outcome is weighted by its probability.
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Payoff x: $0 $500
Probability: 0.999 0.001 $500(0.001) + $0(,999) = $0.50. |
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Variance
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For the set 4, 2, 5, 8, 6, we calculate the mean to be 5.
Then the sum of (x-mean)^2=20 so variance=20/5=4 |
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Standard Deviation
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√Variance
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See Variance.
If variance is 4, standard deviation is √4=2 |
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Standardized Variable (Z-Score)
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Example calculation.
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Sampling Distribution
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The probability distribution of random variables
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Law of Large Numbers
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In the long run, the proportion of outcomes taking any value gets close to the probability of the value. The average outcome gets close to the distribution mean.
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Law of Small Numbers
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The incorrect assumption that short sequences of random events will show the kind of average behavior that occurs only in the long run.
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RandInt(0,100,2)
this will not give us an accurate average of what will happen in the long run |
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Rule for Means
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Rule 1:
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Rule 2:
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Rule for Variances
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Rule 1:
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Rule 2:
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