Download Stat 281 Test 2 Prac..

Stat 281: Intro to Statistics
F2004, Dr. Galster
Test 2 Practice
Name__________________
1. Matching: Fill in the appropriate letters in the blanks below.
A.
B.
C.
D.
E.
F.
G.
H.
I.
J.
K.
Binomial Distribution
Combination
Complementary
Cumulative Distribution Function
Discrete Distribution
Empirical Probability
Event
Exhaustive
Independent
Mean of a Distribution
Mutually Exclusive
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L.
M.
N.
O.
P.
Q.
R.
S.
T.
U.
V.
n-Factorial
Outcome
Probability (in general)
Probability Density Function
Probability Experiment
Random Variable
Sample Space
Subjective Probability
Theoretical Probability
Trial
Variance of a Distribution
The expected relative frequency of an event in the long run
Probability is determined by counting frequency of actual occurrences
Probability determined by analyzing the known characteristics of an experiment
Probability determined on the basis of personal opinion or experience
A repeatable process that yields a recordable result or observation
The smallest unit of an experiment, or one repetition
The immediate or physical result of an experiment
The collection of all outcomes
A subset of the sample space
Two or more events that cannot occur at the same time
Two or more events that, together, make up the whole sample space
Each event contains all the outcomes that are not in the other
The occurrence of one event does not change the probability of another
A function that assigns a numerical value to an outcome of an experiment
Expected Value of X
E( X   )2
n(n  1)(n  2) (2)(1)
The number of ways to choose x objects out of a group of n objects
Fixed number of trials, independent trials, binary response, constant P(success).
2. The following table shows the values for a random variable, X, and the values of its
probability function. Complete the table.
x
0
2
3
5
P( x)
.1
.2
.3
.4
μ
μ2
Sum
Variance
St. Dev. 
3. Sally has some unusual ideas about color coordination. She has a pair of yellow pants
that she will wear with probability 1/3, otherwise she will wear a red pair. She has
three shirts to choose from: yellow, red, and blue. She will not wear the same color
shirt as pants, and she is twice as likely to choose blue as the other available color of
shirt. Make a tree diagram to illustrate the sample space and calculate the probability
she will wear each color of shirt.
4. Suppose P(A)=P(B)=P(C)=.4, P(AUB)=.6, P(AUC)=.8, and P(B∩C)=.16.
a) What is P(A∩B)?
b) What is P(A∩C)?
c) What is P(A|B)?
d) What is P(B|C)?
e) Are A and B mutually exclusive?
f) Are A and C mutually exclusive?
g) Are A and B independent?
h) Are A and C independent?
i) Are B and C independent?
5. Suppose X is a binomial random variable with n=10 and p=0.3. Calculate the
probability that X=0, 1, 2, and more than two. Also give the mean and variance.
6. An urn contains 2 Red marbles, 3 Blue marbles, and 5 White marbles.
a) If an experiment consists of selecting one marble from the jar and recording its
color, give the probability distribution.
b) Suppose two marbles are selected in sequence, with replacement. What is the
probability that both are Blue?
c) Suppose two marbles are selected in sequence, without replacement. What is the
probability that they are different colors?
7. Suppose X is a discrete random variable with only integer values. If P(X>5)=0.6 and
P(X<7)=0.5, what is P(X=6)?
8. Suppose a card game is devised that uses only the cards numbered 10 through Ace
(Ace high). Each player is to be dealt four cards at the beginning of the game.
a) How many different “hands” are there?
b) Find the probability of getting “Four of a Kind.”
9. In the US, there are usually 7 positions for characters available on license plates.
Some states, like South Dakota, use two groups of three, with a space in between, for
most plates. Of course, there are many variations possible.
a) Suppose the 26 letters and 10 digits are available for use in any of the seven
positions. How many combinations are possible?
b) The situation in part a is not often implemented, since it allows for many more
numbers than are needed. Try to make a reasonable guess as to the maximum number
of license numbers a state might need, and explain how you arrived at the number.
Propose a numbering scheme that allows approximately the right number of
combinations for your guess.
c) One of the reasons many states group their numbers into a set of three letters and a
set of three digits is that some letters and numbers look alike, such as the letter O and
zero. Other candidates for confusion are B and 8, I and 1, S and 5, and Z and 2.
Suppose these five letters are eliminated. How many combinations are there now?
d) In South Dakota, the license plate numbers usually start with a two-digit county
code, followed by one letter, and then a group of three digits. How many
combinations are available for each county? Do you think this is “enough?”
10. Also review Test 1 and Test 1 Practice.
Formulas
1
x
N
1
x  x
n
1
MAD   | x  x |
n
1
 2   ( x   )2
N
nk
A
100
d ( Pk )  A.5 or B
xx
z
s
   x P( x)

 2   ( x   )2 P( x)
  x 2 P( x)   2
P( A or B)  P( A B)  P( A)  P( B)  P( A B).
P(A | B) 
P(A B)
P(B)
P(A | B)  P(A) P(A
P(A B)  P(A | B) P(B)
B)  P(A) P(B) (When?)
 n
n!
 
 r  r !(n  r )!
 n
P( x)    p x (1  p) n x ,   np,  2  npq
 x