Graduate (S) Business Administration 502

STATISTICS FOR MANAGERS
Spring 2017
 
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B. Probability and Discrete Probability Distributions

1. Definitions

a. Probability - likelihood or chance that an event will occur

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b. Impossible or null event - no chance of occurring (probability = 0)

c. Certain event - sure to occur (probability = 1)

d. A priori classical probability - based on prior knowledge of process

Probability = X / T

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e. Empirical classical probability - based on observed data

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f. Subjective probability - assigned by a particular person

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2. Probability concepts

a. Simple (marginal) probability - probability of a single event = P(A)

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b. Joint probability - probability of two or more events simultaneously

P(A and B)

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c. Mutually exclusive events - both events cannot occur at same time

P(A and B) = 0

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d. Collectively exhaustive events - one of the events must occur

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e. Addition rule for mutually exclusive events

P (A or B) = P(A) + P(B)

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f. Statistical independence

P (A | B) = P(A)

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g. Multiplication rule for independent events

P(A and B) = P(A) * P(B)

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3. Probability distribution for discrete random variable

  • A listing of all possible numeric outcomes and the probability that they occur

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a. Expected value

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b. Variance and standard deviation

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4. Binomial distribution

a. Properties

(1) Infinite population without replacement, or finite population with replacement

(2) Result is success or failure (mutually exclusive, collectively exhaustive)

(3) p = probability of success, 1 - p = probability of failure

(4) Outcomes are independent

b. Calculation

(1) Formula

  n!  
P(X) = ------------- πX (1 - π)n - X
  X! (n - X)!  

(2) Table

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(3) Spreadsheet

=BINOMDIST(X, n, π, cumulative)

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(4) Range of values

Use addition rule for mutually exclusive events

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c. Characteristics

(1) Shape

May or may not be skewed

(2) Mean

µ = n π

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(3) Variance and standard deviation

σ2 = n π  (1 - π)

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d.   Examples

(1)  Yield or Revenue management

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(2)  Acceptance sampling

  • Accept entire shipment based on testing a sample

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5. Ethical considerations

  • Lack of knowledge about probability

Ex. - Lottery, investment claims