November 23, 2009

• 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 .

• 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.

• 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)?

• 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 1 2 3 4
Prob. 0.1
0.2
0.3
0.3
0.1

• 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?

• 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