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Probability Distribution
The probability distribution for a random variable is an assignment of probability to each of the possible values for the variable
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Probability Distributions
Discrete Probability Distributions 1. The Uniform Distribution; 2. The Binomial Distribution; 3. The Hypergeometric Distribution; and 4. The Poisson Distribution
Continuous Probability Distributions 1. The Uniform Distribution; and 2. The Normal Distribution
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Mean of a Discrete Probability Distribution
The mean of a discrete probability distribution is also called the expected value of the discrete random variable.
where, E(X) = expected value of XX = values of the random variableP(X) = probability of each value of
X
E X XP X( ) ( )
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Standard Deviation of a Discrete Probability Distribution
Standard Deviation of a discrete random variable
where, X = values of the random variable
E(X) = expected value of X P(X) = probability of each value
of X
x SQRT x E x P x ( ) ( )2
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The Binomial or Bernoulli Process
The experiment consists of n identical trials;Each trial results in one of two outcome,
success or failure;The probability of success on a single trial is
equal to p, and remains the same from trial to trial. The probability of failure is ( 1 - p );
The trials are independent; andThe experimenter is interested in X, the
number of successes observed during the n trials.
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Example: Taste Test; Coke Vs. PepsiSample size (n) = 3, P(Coke is preferred) = 0.20
Simple ConsumerEvent One Two Three P(ei)_ ___
e1 C C C (0.20)3 = 0.008
e2 C C P (0.20)2(0.80) = 0.032
e3 C P C (0.20)2(0.80) = 0.032
e4 C P P (0.20)(0.80)2 = 0.128
e5 P C C (0.20)2(0.80) = 0.032
e6 P C P (0.20)(0.80)2 = 0.128
e7 P P C (0.20)(0.80)2 = 0.128
e8 P P P (0.80)3 = 0.512
1.000
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Probability Distribution
Coke Vs. Pepsi_X_ ___ei___ _P(X)_
0 e8 0.512
1 e4,e6,e7 0.384
2 e2,e3,e5 0.096
3 e1 0.008
1.000