Business 90: Business Statistics

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Business 90 Business Statistics Professor
David Mease Sec 03, T R 730-845AM BBC 204
Lecture 15 Start Chapter Some Important
Discrete Probability Distributions
(SIDPD) Agenda 1) Assign Homework 6 (due
Tuesday 4/13) 2) Start Chapter SIDPD
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Homework 6 Due Tuesday 4/13

• 1) Read chapter entitled Some Important
  Discrete Probability Distributions but only
  sections 1-3.
• 2) In that chapter do textbook problems 3, 4,
  14, 15 and 20 (but skip part g in 20)
• 3) Stock X has a mean of 50 and a standard
  deviation of 10. Stock Y has a mean of 100 and
  a standard deviation of 20. Find the mean and
  standard deviation of buying one share of each
• A) If they are independent (so the covariance is
  0)
• B) If the covariance is 30
• C) If the covariance is -30

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Statistics for Managers Using Microsoft Excel
4th Edition

• Some Important Discrete Probability Distributions

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Chapter Goals

• After completing this chapter, you should be able
  to
• Compute and interpret the mean and standard
  deviation for a discrete probability distribution
• Explain covariance and its application in finance
• Use the binomial probability distribution to find
  probabilities
• Describe when to apply the binomial distribution

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Introduction to Probability Distributions

• Random Variable
• Represents a possible numerical value from an
  uncertain event

Random Variables
Discrete Random Variable
Continuous Random Variable
(This Chapter)
(Next Chapter)
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Discrete Probability Distributions
A discrete probability distribution is given by a
table listing all possible values for the random
variable along with the corresponding
probabilities. The appropriate chart to display
it is a bar chart (which has gaps, unlike a
histogram).
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In class exercise 58 A fair coin is tossed two
times. Give the probability distribution and bar
chart for the number of tails.
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In class exercise 59 A fair coin is tossed
three times. Give the probability distribution
and bar chart for the number of tails.
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In class exercise 60 A fair die is rolled
once. Give the probability distribution and bar
chart for the outcome.
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In class exercise 61 A fair die is rolled
twice. Give the probability distribution and bar
chart for the total from the two rolls.
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In class exercise 62 A fair die is rolled
twice. Using your probability distribution from
before answer the following A) What is the
probability that a seven is rolled? B) What is
the probability that the roll is larger than
10? C) What is the probability that an even
number is rolled? D) Given the roll is even, what
is the probability it is a four? E) What is the
probability the roll is even and four? F) What is
the probability the roll is four or odd?
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In class exercise 63 Many people toss a fair
coin two times each. How many tails would you
expect for each person on average?
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Discrete Random Variable Summary Measures

• Expected Value (or mean) of a discrete
• distribution (Weighted Average)

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In class exercise 64 A box contains two 1
bills, one 5 bill and one 20 bill. You reach
in without looking and pull out a single bill.
Give the probability distribution and bar chart
for the amount of money you pull out.
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In class exercise 65 A box contains two 1
bills, one 5 bill and one 20 bill. Many people
reach in without looking and each pull out a
single bill and put it back. On average, how
much money would you expect each person to get?
How much money would you personally be willing to
pay to play this game once?
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In class exercise 66 A fair coin is to be
tossed two times. A) Give the expected number
of tails. B) Give the variance for the number of
tails. C) Give the standard deviation for the
number of tails.
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Discrete Random Variable Summary Measures
(continued)
Variance of a discrete random variable Standar
d Deviation of a discrete random
variable where E(X) Expected value of the
discrete random variable X Xi the ith outcome
of X P(Xi) Probability of the ith occurrence of
X