Question 1

If   
=   
is an initial state vector for the transition matrix T =   
,compute the state vector   
.

Accepted Answer

The answer of If   
=   
is...

Question 2

A biased coin is tossed 8 times.If the probability of heads appearing on any toss is   ,then the probability that exactly six heads appear is

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)    D

Question 3

P(X = 2); n = 10,p =

Accepted Answer

A)  0.1951 
B)  0.2156 
C)  0.1929 
D)  0.0028 
A)  0.1951 
B)  0.2156 
C)  0.1929 
D)  0.0028 A

Question 4

P(X = 6); n = 13,p = 0.5

Accepted Answer

A)  0.2095 
B)  0.3142 
C)  0.2723 
D)  0.0156 
A)  0.2095 
B)  0.3142 
C)  0.2723 
D)  0.0156

Question 5

A random variance X has a distribution given by f(0)= 0.4,f(1)= 0.3,f(2)= 0.3.The variance of X is

Accepted Answer

A)  0.69. 
B)  0.54. 
C)  0.50. 
D)  0.47. 
E)  0.32. 
A)  0.69. 
B)  0.54. 
C)  0.50. 
D)  0.47. 
E)  0.32.

Question 6

Find the steady state vector for the transition matrix T =   
.

Accepted Answer

The answer of Find the steady state vector for the...

Question 7

P(X = 2); n = 5,p = 0.70

Accepted Answer

A)  0.132 
B)  0.198 
C)  0.700 
D)  0.464 
A)  0.132 
B)  0.198 
C)  0.700 
D)  0.464

Question 8

For the transition matrix T =   
,find the probability of going from state 2 to state 1 after three steps.

Accepted Answer

The answer of For the transition matrix T = ...

Question 9

An urn contains 20 marbles,each of which shows a number.Eight marbles show 1,five marbles show 2,and seven marbles show 3.A marble is randomly selected and the number X that shows is observed.The mean of X is

Accepted Answer

A)  1. 
B)    
C)    
D)    
E)    
A)  1. 
B)    
C)    
D)    
E)

Question 10

If X is a binomial random variable involved with six independent trials,and the probability of success on any trial is   ,then the probability that X = 2 is

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 11

If a person watches a certain TV daily evening news program on one evening,then the probability that the person watches that program the next evening is 0.7.However,if the person does not watch the program one evening,then the probability that the person watches the program the next evening is 0.2.
(a)If the person watches the program on Monday,what is the probability that the person watches the program on Wednesday?
(b)If 20% of the population watches the program on Thursday,what percentage can be expected to watch on Friday?

Accepted Answer

The answer of If a person watches a certain TV...

Question 12

A college dining hall has available two fruit juices for breakfast: orange and grapefruit.One hundred students drink juice on a daily basis.It is found that a student will not drink grapefruit juice on two successive days,and if a student drinks orange juice one day,then the following day the student is equally likely to drink orange juice as to drink grapefruit juice.If 40 of the regular juice drinkers drink orange juice on Monday,how many can be expected to drink orange juice on Wednesday?

Accepted Answer

A)  10 
B)  30 
C)  50 
D)  60 
E)  90 
A)  10 
B)  30 
C)  50 
D)  60 
E)  90

Question 13

If   is a transitional matrix for a Markov chain,determine the value of b.

Accepted Answer

A)  0.1 
B)  0.2 
C)  0.4 
D)  0.6 
E)  0.8 
A)  0.1 
B)  0.2 
C)  0.4 
D)  0.6 
E)  0.8

Question 14

Suppose that you pay $3 to play a game in which a fair die is rolled.You receive the number of dollars equal to the number of dots that appear.What is your expected gain (or loss)on each play?

Accepted Answer

The answer of Suppose that you pay $3 to play...

Question 15

At the time of purchase of its product,a company offers a contract to its customers that guarantees the replacement of the product if it malfunctions within a one-year period.The cost of the contract is $10.The probability that a unit of the product malfunctions within one year of purchase is 0.06.If the cost to the company for replacement of a unit is $160,determine the company's expected gain or loss per contract.

Accepted Answer

gain of $0

Question 16

A platypus net is set out on four successive days where a capture-recapture study is located.Only 1 platypus can be netted per day,and the probability that a platypus will enter the trap and be netted is   
.If X is the number of platypuses captured over the four days,find the distribution of X.

Accepted Answer

The answer of A platypus net is set out on...

Question 17

From a standard deck of 52 playing cards,two cards are randomly drawn in succession without replacement.If X is the number of red cards that are drawn and f is the distribution of X,find f(0),f(1),and f(2).

Accepted Answer

f(0)= @#IMG-DLM&_TB6578_11 ; f

Question 18

If   is a transition matrix for a Markov chain,determine the values of a,b,and c.

Accepted Answer

A = 0.1,B

Question 19

Find the steady state vector for the transition matrix T =   
.

Accepted Answer

The answer of Find the steady state vector for the...

Question 20

Suppose T =   is the transition matrix for a Markov chain.If Q =  
Is the steady-state vector,find

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

If = is an initial state vector for the transition matrix T = ,compute the state vector .

A biased coin is tossed 8 times.If the probability of heads appearing on any toss is ,then the probability that exactly six heads appear is

P(X = 2); n = 10,p =

P(X = 6); n = 13,p = 0.5

A random variance X has a distribution given by f(0)= 0.4,f(1)= 0.3,f(2)= 0.3.The variance of X is

Find the steady state vector for the transition matrix T = .

P(X = 2); n = 5,p = 0.70

For the transition matrix T = ,find the probability of going from state 2 to state 1 after three steps.

An urn contains 20 marbles,each of which shows a number.Eight marbles show 1,five marbles show 2,and seven marbles show 3.A marble is randomly selected and the number X that shows is observed.The mean of X is

If X is a binomial random variable involved with six independent trials,and the probability of success on any trial is ,then the probability that X = 2 is

If is a transitional matrix for a Markov chain,determine the value of b.

Suppose that you pay $3 to play a game in which a fair die is rolled.You receive the number of dollars equal to the number of dots that appear.What is your expected gain (or loss)on each play?

A platypus net is set out on four successive days where a capture-recapture study is located.Only 1 platypus can be netted per day,and the probability that a platypus will enter the trap and be netted is .If X is the number of platypuses captured over the four days,find the distribution of X.

From a standard deck of 52 playing cards,two cards are randomly drawn in succession without replacement.If X is the number of red cards that are drawn and f is the distribution of X,find f(0),f(1),and f(2).

If is a transition matrix for a Markov chain,determine the values of a,b,and c.

Find the steady state vector for the transition matrix T = .

Suppose T = is the transition matrix for a Markov chain.If Q = Is the steady-state vector,find

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Exam 10: Additional Topics in Probability

If = is an initial state vector for the transition matrix T = ,compute the state vector .

A biased coin is tossed 8 times.If the probability of heads appearing on any toss is ,then the probability that exactly six heads appear is

P(X = 2); n = 10,p =

P(X = 6); n = 13,p = 0.5

A random variance X has a distribution given by f(0)= 0.4,f(1)= 0.3,f(2)= 0.3.The variance of X is

Find the steady state vector for the transition matrix T = .

P(X = 2); n = 5,p = 0.70

For the transition matrix T = ,find the probability of going from state 2 to state 1 after three steps.

An urn contains 20 marbles,each of which shows a number.Eight marbles show 1,five marbles show 2,and seven marbles show 3.A marble is randomly selected and the number X that shows is observed.The mean of X is

If X is a binomial random variable involved with six independent trials,and the probability of success on any trial is ,then the probability that X = 2 is

If is a transitional matrix for a Markov chain,determine the value of b.

Suppose that you pay $3 to play a game in which a fair die is rolled.You receive the number of dollars equal to the number of dots that appear.What is your expected gain (or loss)on each play?

A platypus net is set out on four successive days where a capture-recapture study is located.Only 1 platypus can be netted per day,and the probability that a platypus will enter the trap and be netted is .If X is the number of platypuses captured over the four days,find the distribution of X.

From a standard deck of 52 playing cards,two cards are randomly drawn in succession without replacement.If X is the number of red cards that are drawn and f is the distribution of X,find f(0),f(1),and f(2).

If is a transition matrix for a Markov chain,determine the values of a,b,and c.

Find the steady state vector for the transition matrix T = .

Suppose T = is the transition matrix for a Markov chain.If Q = Is the steady-state vector,find

Review of Algebra

Applications and More Algebra

Functions and Graphs

Lines parabolas and Systems

Exponential and Logarithmic Functions

Mathematics of Finance

Matrix Algebra

Linear Programming

Introduction to Probability and Statistics

Limits and Continuity

Differentiation

Additional Differentiation Topics

Curve Sketching

Integration

Methods and Applications of Integration

Continuous Random Variables

Multivariable Calculus

Filters