Download 6.1 Discrete vs Continuous Random Variables

6.1 Discrete vs Continuous Random Variables
Define the following(p. 260/261):
Random Variable-
Discrete Random Variable-
Continuous Random Variable-
Determine which are discrete vs continuous and indicate possible values that they could take:
Shoe size:
Foot length:
Student’s age:
Number of birthdays he/she had:
6.1 Discrete Random Variables
In 2010, there were 1319 games played in the National Hockey League’s regular season.
Imagine selecting one of these fames at random and then randomly selecting one of the two
teams that played in the game. Define the random variable X = number of goals scored by a
randomly selected team in a randomly selected game. The table below gives the probability
distribution of X:
Goals:
0
Probability: .061
1
.154
2
.228
3
.229
4
.173
5
.094
6
.041
7
.015
8
.004
9
.001
a. (p. 262) Show that the probability distribution for X is legitimate.
b. (p. 263) Make a histogram of the probability distribution and describe what you see.
c.
(p. 264) What is the probability that the number of goals scored by a randomly selected
team in a randomly selected game is at least 6? Use correct notation!
d. Compute the mean (or expected value) of the random variable X and interpret this
value in context. (p. 265)
e. Compute using the definition formula and interpret the standard deviation of the
random variable X. (p. 267)
f.
Determine if X=9 is an unusual number of goals during this season (p. 269)
g.
Construct a probability distribution graph marking the distances away from the mean.
6.1 Winning and Losing at Roulette
Example 2: Another wager players can make in roulette is called a “corner bet”. To make this
bet, a player places his chips on the intersection of four numbered squares on the roulette
table. If one of these numbers comes up on the wheel and the player bet $1, the player gets his
$1 back plus $8 more. Otherwise, the casino keeps the original $1 bet. If X=net gain from a
single $1 corner bet, what are the possible outcomes?
What is the probability distribution?
Value
Probability
Graph the probability distribution.
What is the player’s average gain? Interpret this value.
What is the standard deviation of X? Interpret this value.