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Probability

Queueing Theory : Swimmers and Exponential Distribution

Queueing Theory Question 1 An average of 10 people per hour arrive (inter-arrival times are exponential) intending to swim laps at the local YMCA. Each intends to swim an average of 30 minutes. The YMCA has 3 lanes open for lap swimming. If one swimmer is in a lane, he or she swims up and down the right side of the lane.

Stochastic Processes : Poisson Process and Markov Chains

1. Suppose that shocks occur according to a Poisson process with rate A> 0. Also suppose that each shock independently causes the system to fail with probability 0 < p < 1. Let N denote the number of shocks that it takes for the system to fail and let T denote the time of the failure. (a) FindP{T>tNrrn}. (b) FindP{NrrnT=t}. (

Statistics : Standard Deviation and Mean (10 Problems)

1. True or False? The standard deviation of a population will always be smaller than the standard deviation of the sample means (of the samples used to estimate this same population). 2. The mean height for a population is 65 inches and the standard deviation is 3 inches. Let X_ denote the mean height for a sample of people

Statistics : Probability of Winning a Powerball Lottery

The Powerball For a single ticket, a player first selects five numbers from the numbers 1-53 and then chooses a powerball number, which can be any number between 1 and 42. A ticket costs $ 1. In the drawing, five white balls are drawn randomly from 53 white balls numbered 1-53, and one red Powerball is drawn randomly from

Probability

The sign "I LOVE MATHEMATICS" is put on the wall of the mathematics building at South Central Carolina Technical College. The letters start to fall off of the sign. Find the probability of each of the following events. 1.. The first letter that falls off is "M" . 2. The second letter that falls off is an "A" knowing tha

18 Problems : Payoff Tables and Decision Trees; Control Charts; Bayes Theorem; Total Quality Management ( Demings 14 Points of Management ), Expected Monetary Value, Red Bead Experiment

1. A tabular presentation that shows the outcome for each decision alternative under the various states of nature is called a: a. payback period matrix. b. decision matrix. c. decision tree. d. payoff table. 2. The difference between expected payoff under certainty and expected value of the best act without certainty is

Various Statistics Problems

1. Event A: You spend your entire Memorial Day 2006 in Acapulco. Event B: You spend your entire Memorial Day 2006 with some of your friends. TRUE OR FALSE: A and B are mutually exclusive events. 2.Event A: You spend your entire Memorial Day 2004 in Denver. Event B: You spend your entire Memorial Day 2004 in Vermont. TRU

Independent random variables

1. A coin is tossed 3 times. Discrete random variable X is equal to the number of times Heads comes up. Discrete random variable Y has the value 1 if the first toss comes up heads and 0 otherwise. (a) Find Pr[(X=1)n(y=1)] Are X and Y independent random variables?

Probability - drawing tokens

7. There are some tokens in a bag. Each token has a number ( a positive integer) printed on it. Ernesto does not know how many tokens are in the bag, and the only thing he knows about the numbers on them is that the mean of the numbers is 3 and the variance is 2. Ernesto is going to play a game in which he draws 1 token from th

Probability density function

5. Let E be the event that the number which comes up when a single die is tossed is divisible by 3. Let X be the number of times that event E occurs in 3 tosses of the die. (a) Make a table showing the pdf and the cdf of X. (b) Find E(X) and V(X).

Probability - cards

4. A hand of 5 cards contains 2 red cards and 3 black cards. Trish plays the following game: A card is drawn from the hand. If the card is red, the game stops immediately. If the card is black, this black card is set aside and a red card is put into the hand in its place. Then another card is drawn from the hand and the same pro

Solution please

3. There are 13 standard decks of cards. Each deck is shuffled, separately. The 13 decks are lined up in a row on the table. The top card is drawn from each deck. What is the probability that at least 3 cards of each suit are drawn?

Probability

1. There are 3 boxes. Each box contains several envelopes. Some envelopes have "you lose" written on them. The rest say "you win..." . However, of the ones that say "you win..." , some contain only a piece of paper saying "... nothing" . Each of the other contains a $5 bill. The first box contains 3 "lose" envelopes and 2 so-

Probabilities

Problem 4. Let X denote the number of boys in a family with four children. Pr(X > 3) is? a. 5/16 b. ¼ c. 11/16 d. 2/3 e. None of the above

Probability & Statistics : Chebychev Inequality

Suppose that a probability distribution has a mean 20 and standard deviation 3. The Chebychev inequality states that the probability that an outcome lies between 16 and 24 is: a. less than 7/16 b. at least 7/16 c. at most 1/4 d. at least 1/4 e. none of the above

Probability & Statistics : Outcome of Dice Rolls

Two people play a game. A single die is thrown. If the outcome is a 2 or a 3, then player A pays player B $6.00. How much should B pay A when a 1, 4, 5, or 6 is thrown so that A and B break even, on average, over many repititions of the game? a. $2.00 b. $8.00 c. $4.00 d. $6.00 e. None of the above

Probability & Statistics : Quartiles

The test scores of 30 students are listed Below. Find Q3; 31 41 45 48 52 55 56 56 63 65 67 67 69 70 70 74 75 78 79 79 80 81 83 85 85 87 90 92 95 99

Sets, Counting and Probability : Events

A light Bulb manufacturer tests a light bulb by letting it burn until it burns out. The experiment consists of observing how long (in hours) the light bulb burns. Let E be the event "the bulb lasts less than 100 hours", F be the event "the bulb lasts less than 50 hours",and G be the event "the bulb lasts more than 120 hours." T

Probablity

P(8,5) = a. 5!/8! b. 8*7*6*5*4 c. 8*7*6*5 d. 8!/5!3!

Probability : Combinations of Three-Numbered Spinners

Given two spinners divided into three equal parts. The first spinner is numbered 1- 2- and 3. The second spinner is numbered 4 - 5 - and 6. a. If each spinner is spun once, what is the probability that the product of the two numbers spun is even? b. What is the probability that the sum of the two is even?

Probability : Selection Without Replacement

John randomly picks (without replacing) four marbles from a jar that contains 6 red and 4 blue marbles. Mary randomly picks three marbles from a jar that contains 3 red and 5 blue marbles. What is the probability that John picks more blue marbles than Mary?

Unbiased bits per flip

Hi I would appreciate if you could help me with this question. Q. A coin that comes up heads with probability 3/4 on each flip can be used to generate more unbiased bits per flip ( on average ) than a coin that comes up heads with probability 7/8. Is it TRUE or FALSE and How ? Thanks

Frequencies of Dice Roll Combinations and Probabilities of Dice Rolls

When a pair of dice is rolled, the total will range from 2 (1,1) to 12 (6,6). It is a fact that some numbers will occur more frequently than others as the dice are rolled over and over. A. Why will some numbers come up more frequently than others? B. Each die has six sides numbered from 1 to 6. How many possible ways can a nu

Statistics z test probability

Packages from packing machine have a mass, which is normally distributed with mean 200g and standard deviation 2g. Find the probability that the package from the machine weighs a) less than 197g b) more than 200.5g (use standard normal variable Z and normal distribution tables)