(See attached file for full problem description) Two fair dice have both had two of their sides painted red, two painted black, one painted yellow and one painted white. (a) when this pair of dice is rolled, what is the probability that both will show the same color? (b) What is the probability that only one of the dice wil
Suppose a worker needs to process 400 items. The time to process each item is exponentially distributed with a mean of 2 minutes, and the processing times are independent. Approximately, what is the probability that the worker finishes in less than 7 hours?
Let X be a Poisson random variable with parameter 5, and let Y = min(X,5). (a) What is the p.m.f. of X? (b) What is the mean of X? (c) What is the variance of X? (d) What is the p.m.f. of Y (e) Compute E[Y}.
8. A sample of 2,000 licensed drivers revealed the following number of speeding violations. Number of Violations Number of Drivers 0 1,910 1 46 2 18 3 12 4 9 5 or more 5 Total 2,000 1. What is the experiment? 2. List one possible event. 3. What is the probability that a particular driver had
1. Each vehicle in Mexico is either a truck, car or bicycle. Also each vehicle is red, green or yellow. We pick a vehicle at random. The following are known facts: 1. There's a 30% chance that vehicle is truck 2. There's 50% chance that vehicle is red 3. There's 20% chance that vehicle is a red truck 4. The vehicle is
Assume the probability that you will make a sale on any given phone call is 0.78. Find the probability that you (a) make your first sale on the 4th call, (b) make your first sale on the first, second, third, or fourth call, and (c) you do not make a sale on one of the first 4 calls.
Piggy Bank would like to examine the required sample size needed to be able to estimate the mean dollars that each card holder will spend each month. It would like to be within plus or minus $10 of the true mean with a 98% confidence level. The standard deviation is thought to be $500. How many card holders should be sampled? Af
Concerning the problem below, I understand that one event must occur to have collectively exhaustive event. I don't understand how to determine the problem as stated. If two events are collectively exhaustive, what is the probability that both occur at the same time? a. 0 b. 0.50 c. 1.00 d. Can't be determined from the i
Two airlines offer conveniently scheduled flights to the airport nearest your corporate headquarters. Historically, flights have been scheduled as reflected in this transition matrix. Current Flight Next Flight Airline A Airline B Airline A .6 .4 Airline B .2 .8 If your last flight was on B, what is the probabili
(See attached file for full problem description) --- 1. A food distributor carries 64 varieties of salad dressing. Appleton Markets stocks 48 of these flavors. Beacon Stores carries 32 of them. The probability that a flavor will be carried by Appleton or Beacon is 15/16. Find the probability a flavor is carried by both A
You are taking a multiple-choice quiz that consists of 3 questions. Each question has 4 possible answers, only one of which is correct. To complete the quiz, you randomly guess the answer to each question. Find the probability of guessing (a) exactly 2 answers correctly, (b) at least 2 answers correctly, or (c) less than 2 answe
In a city, 60% of the voters are in favor of building a new park. An interviewer intends to conduct a survey. a. If the interviewer selects 20 people randomly, what is the probability that more than 15 of them will favor building the park? b. Instead of choosing 20 people as in part a, suppose that the interviewer wants t
A consumer is contemplating the purchase of a new compact disc player. A consumer magazine reports data on the major brands. Brand A has lifetime (TA) which is exponentially distributed with m=.02; and Brand B has lifetime (TB) which is exponentially distributed with m=.01. (The unit of time is one year). a. Find the expec
Independence of random variables. See attached file for full problem description.
Let X1, X2,... be i.i.d. random variables with p.g.f Gx(s) and N be a r.v independent of X with p.g.f. Gn(s). Define S=X1+X2+...+XN. Find Var(S) in terms of expectations and variances of X and N.
Parameter Distribution. See attached file for full problem description.
1. Prove that for all x > 0 (1/x - 1/x^1)phi(x) < 1 - ohi(x) < (1/x)phi(x) Hint: Integrate the following inequalities: (1 - 3y^-4)e^(y^2/2) < e^-(y^2)/2 < (1 + y^-2)e^-(y^2)/2. 2. Let X be a random number from (0,1) (ie. X ~ uniform (0,1)). Find the density function of (a) Y _ -log(1-X), (b) Z _ X^n. See attachment f
In a sample of 2400 people, 170 have blonde hair. Two unrelated people are selected at random... (See attached file for full problem description)
(See attached file for full problem description) --- 1. A study determines that 60% of the voters in a town intend to vote for the incumbent mayor. If a sample of 8 people is selected, the approximate probability that 6 of the 8 people surveyed intend to vote for the incumbent is (using the binomial probability formula): a.
The probability that a flower seed will germinate is 0.7. Find the mean and standard deviation for the random variable x, the number of seed that will germinate in each set. Seeds are planted in sets of 11.
A card is picked up at random from a standard deck of 52 cards.Find the odds that the card is a heart.
Consider a gambler who at each play of the game has probability of winning one unit and probability of loosing one unit. Assuming that the successive plays of the game are independent, what is the probability that, starting with units, the gambler's fortune will reach
1. Suppose you have 3 nickels, 2 dimes, and 6 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 half-dollar? c. You will draw a quarter? 2. You are rolling a pair of dice, one red and one green. What is the probability
A) A shipping form keeps 2 cars in readiness for local delivery. Because of demands on their time and the frequency of mechanical failure, the probability that a particular car will be available when needed is 0.9. The availability of one car is independent of the availability if other. a) If both cars are wanted at the sam
Records of a department store show that 5% of customers who make a purchase return the merchandise for refund. Of the remaining customers, 9% return the mechanise in order to exchange it. a) In the next six purchase, what is the probability that at most one will return for refund? b) In a sample of eight customers, exactly
Suppose that an executive of a venture capital investment firm is trying to decide how to allocate his funds among three different projects, each of which requires a $100,000 investment. The projects are such that one of the three will definitely succeed, but it is not possible for more than one to succeed. Looking at each p
Working on below problem to identify error as presented. "On the fictitious game show "Marginal Analysis for Everyone" the host subjects contestants to unusual tests of mental skill. On one, a contestant may choose one of two identical envelopes labeled A and B, each of which contains an unknown amount of money. The host
Trying to complete the below word problem but not sure how to solve. ________________ It is said that Napoleon assessed probabilities at the battle of waterloo in 1815. his hopes for victory depended on keeping the English and Prussian armies seperated. Believing that they had not joined forces on the morning of the fatefu
The following payoff matrix is given in dollars: Event Probability Action A Action B 1 0.5 400 700 2 0.5 200 500 Referring to the table, what is the optional action using the EMV criterion? A. Action A B. Action B C. Either Action A or Action B D. It cannot be determined from the information given
The following payoff matrix is given in dollars: Event Probability Action A Action B 1 0.5 400 700 2 0.5 200 500 Referring to the table, the return to risk ratio for Action B is A. 0.167 B. 3.0 C. 6.0 D. 9.0