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Random Variables
November 23, 2009
Discrete Random Variables
• A random variable is a variable whose
value is a numerical outcome of a random
phenomenon.
• When each value of a random variable
can be assigned a probability, the random
variable is discrete.
Probability Distributions
• This list of probabilities assigned to each
possible value of a random variable X is
called the probability distribution of X.
• The probability distribution can be written
as a table, or as a histogram (called a
probability histogram).
• In order to be a legitimate probability
distribution, the probabilities must fall
between 0 and 1 and sum to 1.
Example 1 (Uniform Distribution)
• Imagine picking a digit from the (infinite)
decimal expansion for . Let X be the
random variable whose value is the digit
you pick. The probability for each digit is
equally likely.
• Find the probability distribution and make
a probability histogram. What is P(X > 3)?
Example 2
• Spell-checking catches “nonword errors,”
which result in a string of letters that is not a
word (such as “teh” for “the”).
• Let X represent the number of nonword
errors in a 250 word essay.
• The variable X has the following probability
distribution:
errors 0
Prob. 0.1
1
0.2
2
0.3
3
0.3
4
0.1
Example 2 Continued
• Verify that this gives a legitimate
probability distribution.
• Write the event “at least one nonword
error” in terms of X. What is the
probability of this event?
• Describe the event X ≤ 2 in words. What
is the probability that X < 2?
Assignment
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Page 461: 7.2,7.3 and 7.4
Page 475: 7.7 and 7.8
Page 477: 7.12,7.14,7.15 and 7.20
Due Wednesday