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College Mathematics

Exercises on Sets 1. Please provide a short definition of the following: a. Set b. Subset c. Proper Subset d. Complement of a set e. Union of a set f. Intersection of a set Solve following problems showing your work: 2. Set X = {3, 7, 11, 21, 39, 43, 567}, Set Y = {1, 3, 6, 8, 11, 42, 567}

Joint Probability Shown

Please give step-by-step process for solving the following problem. Suppose that X and Y are continuous random variables with joint pdf (probability distribution function) fXY(x,y) = kx^2y, when 0 < x < y < 1, 0, otherwise. (a) Determine the value of k. (b) Find P(X+Y > 1).

Exponential Distribution: Probability distribution function

Please give step-by-step process for solving the following probability problems. Let X ~ Exp(lamda1) and that Y ~ Exp(lambda2). Further assume that X and Y are independent. (a) Write down the joint pdf (probability distribution function) of X and Y, fXY(x,y). (b) For t > 0, prove that P(Y < tX) = t lambda2 / ( lambda1 +

Stock Probability

Please explain how to solve this problem. An investment advisor recommends the purchase of shares in Probaballisitics, Inc.. He has made the following predictions: P(Stock goes up 20% | Rise in GDP) = .6 P(Stock goes up 20% | Level GDP) = .5 P(Stock goes up 20% | Fall in GDP) = .4 An economist has predicted that the p

Biased Bernoulli Process

Suppose that two teams that meet in the world series are closely matched: the better team wins a given game with a probability of .55. What is the probability that the better team will win the World Series? Treat the games as tosses of a biased coin. Express the event "the better team wins" in terms of elementary Bernoulli event

probability of a company's stock price

The average stock price for companies making up the S&P 500 is $30,and the standard deviation is $8.20. Assume the stock prices are normally distributed. a. What is the probability that a company will have a stock price of at least $40? b. What is the probability that a company will have a stock price no higher than $20?

Poisson arrival, Exponential service time

The Friendly Neighbor Grocery Store has a single checkout stand with a full-time cashier. Customers arrive randomly at the stand at a mean rate of 30 per hours. The service-time distribution is exponential, with a mean of 1.5 minutes. This situation has resulted in occasional long lines and complaints from customers. Therefore,

Sets and probability of marble drawn from a box

28. A marble is drawn from a box containing 3 yellow, 4 white, and 8 blue marbles. Find the odds in favor of drawing the following. a. A yellow marble b. A blue marble c. A white marble If two cards are drawn without replacement from an ordinary deck, find the probabilities of the following results 8. The second is blac

From a Probability and Statistics math class

5. The fracture strength of tempered glass averages 14 (measured in thousands of pounds per square inch) and has standard deviation 2. a. What is the probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.5? b. Find an interval that includes, with probability 0.95, the avera

Expected Cash Flow and Net Present Value

Cooper Construction is considering purchasing new, technologically advanced equipment. The equipment will cost $625,000 with a salvage value of $50,000 at the end of its useful life of 10 years. The equipment is expected to generate additional annual cash inflows with the following probabilities for the next ten years: Proba

Statictis Problems

These are some of the questions I've run into and need help for. I'm unable to solve some of these problems. I'm studying for my final next week and I'm preparing for that. 7.16 Daily output of Marathon's Garyville, Louisiana, refinery is normally distributed with a mean of 232,000 barrels of crude oil per day with a s


1. Suppose you have 4 nickels, 6 dimes, and 4 quarters in your pocket. If you draw a coin randomly from your pocket, what is the probability that a. You will draw a dime? b. You will draw a nickel? c. You will draw a quarter? 2. You are rolling a pair of dice, one red and one green. What is the probability of

Probability Questions Described

Using a deck of 52 cards (13 red numbered 1-13, 13 blue numbered 1-13, 13 green numbered 1-13 and 13 black numbered 1-13): 1. describe the steps neccessary to calculate the theroretical probability of a) drawing 2 red cards one after another (with replacement)from a given deck b) drawing 3 cards with the same value withou

Small questions

1. A particular spell has a .18 (i.e. 18%) chance to do critical damage. What is the probability that a spell can be cast 10 times in a row without doing critical damage? A) .137 B) .820 C) .862 D) <.001 2. What is the probability of the sum of two dice equaling an odd number? A) .50 B) .38 C) .25 D) .61 3. A coin


Suppose that you select 2 cards without replacement from an ordinary deck of playing cards. a. If the first card that you select is a king, what is the probability that the second card that you select is a heart? b. If the first card that you select is a heart, what is the probability that the second card that you select

Probability: Problems and Solutions

1. How many ways are there of drawing a red, a black, and a green ball from a bucket with 2-Red, 2-Black, and 5-Green balls? 2. What is the probability of drawing exactly one ball of each color if you select 3 balls from the bucket above?


Employees of a company fall into four categories: Managers (4%), Administrators (12%), Technicians (26%) and Labourers (58%). If 20% of the Managers, 5% of the Administrators, 3% of the Technicians and 0.5% of the Labourers have the opportunity of promotion in the next year: (i) What is the probability that a randomly chose

Premutations, probability, variance, data display

Please make examples thorough enough at least 100 words each response. In your own words what is the difference between permutations and combinations? I need 3 real world examples of where order matters in a choice â?¦.and have to make and 3 examples of choices where order does not matter. What are some of the benefits

Probability Question

Topic 18 Exp 3 The following table contains information on the 2002 resident population of the U.S., by age. (Source: The New York Times Almanac 2004, page 277.)

Probability in a Multiple Choice Quiz

Cass is taking a 5 question multiple-choice quiz in which each question has 3 choices. He guesses o all of the questions. (a) What is the probability that Cass answers all of the questions correctly? (B) What the probability that he answers 3 questions correctly?

Probability questions

7. Suppose that you are dealt a hand of 9 cards from a standard deck of 52 playing cards. a. What is the probability that you are dealt exactly 3 kings? b. What is the probability that you are dealt 9 cards of the same suit? c. What is the probability that you are not dealt at least 2 cards of each suit? 11.

Determining Probability: Diagnostic Test for Cancer

Suppose that there is a diagnostic test for a particular type of cancer. Given that the person has this type of cancer, the probability that the test would be positive is 95%. However, if the person does not have this type of cancer, then the probability that the rest will be positive is 1%. Suppose that 2% of the population hav

Standard Deviation Probability

The probability that a certain basketball team will win a given game is .62. If the team plays 50 games, find the expected number of wins and the standard deviation. (Round to the nearest hundredth if necessary.)

Decision Analysis

1. The following payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature: State of Nature Decision Alternative S1 S2 S3 D1 250 100 25 D2 100 100 75 A. Construc

Cumulative Probability- Arrival Lag

Consider the table given below. Cumulative Probability Arrival Lag (in minutes) Probability 0.2 5 0.2 0.5 10 0.3 1.0 15 0.5 a. If rand() = 0.31752, what i

theoretical probability

1. The theoretical probability of undesirable side effects resulting from taking Pyrene is 1 in 15. If 60 people take Pyrene to relieve congestion, theoretically how many will encounter undesirable side effects? 2. A bag contains 16 yellow marbles, 6 green marbles, and 7 red marbles. What is the chance of drawing a yellow ma

binomial distribution with parameters

Suppose only 70% of all drivers in a certain state regularly wear a seat belt. A random sample of 500 drivers is selected. What is the probability that: a) between 320 and 370 (inclusive) of the drivers in the sample regulary wear a seat belt b) Fewer than 325 of those in the sample reqularly wear a seat belt? Fewer than 3

Probability: Hauling Concrete Example Question

The cycle time for trucks hauling concrete to a highway construction site is uniformly distributed over the interval 40 to 60 minutes, what is the probability that the cycle time exceeds 55 minutes if it is known that the cycle time exceeds 45 minutes?


If the annual proportion of erroneous income tax returns filed with the IRS can be looked upon as a random variable having a beta distribution with &#945;= 2 and &#946; = 9, what is the probability that in any given year there will be fewer than 10 percent erroneous returns

Probability and sequence

5. If Kate starts on the paving stone outside her house and hops onto every second stone, she will get to the second to last stone before the house of her friend Sam. (see diagram) If Kate now turns round on this stone and hops onto every third stone, she will get back to the third stone. (see diagram) Kate turns