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Chapter 6 – “Random Variables”
6.1 – Discrete & Continuous Random Variables
By the end of this section, you should Be aBle to do…
• Calculate and interpret the standard deviation of a discrete
random variable.
• Compute probabilities using the probability distribution of a
continuous random variable.
Variance of any discrete random variable X:
𝜎𝑋2 = 𝑉𝑎𝑟ሺ𝑋ሻ =
Standard deviation of any discrete random variable X:
Be mindful of your notation!
Example 6.7: What are typical Apgar scores (see page 349 for a
description)? Consider the random variable X = Apgar Score.
Compute the standard deviation of the random variable X and
interpret it in context.
Example 6.8: In an earlier example, we defined the random
variable X to be the number of languages spoken by a randomly
selected U.S. high school student. The table below gives the
probability distribution of X:
Compute the standard deviation of the random variable X and
interpret this value in context.
C.Y.U. – Page 355
A large auto dealership keeps track of sales made during each
hour of the day. Let X = the number of cars sold during the first
hour of business on a randomly selected Friday. Based on
previous records, the probability distribution of X is as follows:
1. Compute and interpret the mean of X.
2. Compute and interpret the standard deviation of X.
Suppose we want to use our graphing calculators to randomly
generate numbers between 0 and 1. Can we count them all?
Our sample space is simply
S = all numbers between 0 and 1.
Continuous random variable X:
The probability of any continuous event is
Example 6.9: The weights of 3-year-old females closely follow
a Normal distribution with a mean of 𝜇 = 30.7 pounds and a
standard deviation of 3.6 pounds. Randomly choose one 3-yearold female and call her weight X. What is the probability that a
randomly selected 3-year-old female weighs at least 30 pounds?
Discrete vs. Continuous Random Variables (recap)
Homework: Page 360 - 362 #14, 16, 17, 18, 22, 24, 26