Download MATH 110 Test Three Outline of Test Material EXPECTED VALUE

MATH 110 Test Three Outline of Test Material
EXPECTED VALUE (8.5)
 Super easy ones
(when the PDF is already given to you as a table and all you need to
do is multiply down the columns and add across)
Example: Find the expected value of the random variable X.
X
2
4
6
7
P(X)
0.3
0.2
0.1
0.4
EXPECTED VALUE (8.5)
 Still easy but the probabilities are given graphically
Example:
Find the expected value of the
random variable X.
EXPECTED VALUE (8.5)

Still easy but the probabilities are given in a ‘word problem’.
Example: A wedding photographer has a big event that will yield a
profit of $2000 with a probability of 0.8 or a loss (due to
unforeseen circumstances) of $500 with a probability of 0.2.
What is the photographer’s expected profit?
EXPECTED VALUE (8.5)
 Lotteries, Raffles, etc.
(Practice makes perfect. Please do a lot of these. I posted lots of
problems like these…including some YouTube videos.)
Example: Suppose you buy 1 ticket for $2 in a lottery with 1000 tickets.
The prize for the one winning ticket is $300. What are your expected
winnings?
EXPECTED VALUE (8.5)
 Lotteries, Raffles, etc.
Example: Find the expected payback for a game in which you bet
$4 on any number from 0 to 199 if you get $400 if your number
comes up.
EXPECTED VALUE (8.5)
 Lotteries, Raffles, etc.
Example: In roulette, there are 18 red compartments, 18 black
compartments & 2 compartments that are not red or black.
If you bet $2 on red and the ball lands on red, you get to keep the
$2 you paid to play and you win another $2. Otherwise, you lose
your $2 bet. What is your expected payback if you bet $2 on red?
BASIC STATISTICS (9.1 & 9.2)
 Easy…mode, median, mean, range and standard deviation
Example: For the following set of numbers, find the mode, the
median, the mean (round to nearest tenth), the range and the
standard deviation (round to the nearest hundredth):
41 60 56 35 40 36
BASIC STATISTICS (9.1 & 9.2)
 Mean and standard deviation from a Frequency table
Example: Find the mean (round to the nearest tenth) and standard
deviation (round to the nearest hundredth) of the placement
scores in the table below.
Value
4
7
8
3
Frequency
3
2
1
4
BASIC STATISTICS (9.1 & 9.2)
 Grouped means and standard deviations
Example: Find the mean (round to the nearest tenth) and standard
deviation (round to the nearest hundredth) of the data below:
Interval
1-4
5-8
9-12
13-16
Frequency
3
2
1
4
BASIC STATISTICS (9.1 & 9.2)
 Chebyshev’s Theorem
Example: Find the fraction of all the numbers of a data set that
must lie within 3 standard deviations from the mean.
BASIC STATISTICS (9.1 & 9.2)
 Chebyshev’s Theorem
Example: In a certain distribution, the mean is 50 with a standard
deviation of 6. Use Chebyshev’s Theorem to find the probability
that a number lies between 26 and 74. Write your final answer
rounded to the nearest thousandth.