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Please see attached document. If an individual with initial wealth w that is facing a random risk X that takes values è with probability p and value zero with probability 1 - p. If the individual does not take insurance, his wealth will be w - X. If he takes insurance, his wealth will be w - a, where a is the insurance pr

Probability: bernoulli trial model

Use the Bernoulli model to solve: A) Calculate probabilites of gettin from 0 to 5 clubs on a hand B) What is the probabilty of gettin 2 or fewer cubs of 5 cards?

Probabilty: solve using Bayes Theorem

An admissions committee must select students for an MBA program. Past data show that 70% of students complete (C) the program. It is also known that 50% of the graduating students scored above 500 (A) on the GMAT test. While 20% of the dropouts (D) scored that well. Consider a new MBA student. A) What is the prior probabilty

Probability, solve using methods of probability in a poker game

Poker, in the deck 52 cards, hand of 5 cards, one of the winning hands is flush, all cards belong to a common suit. A) Calculate the number of possible combinations of poker hands B) Calculate a probabilty of flush C) Calculate a probabilty of getting 4 aces on one hand D) calculate a probabilty of getting 2 aces or


In one math class of college there aer 10 males and 20 females. The professor makes 3 student teams to work on a group project. A) How many possible teams can be made? B) What is a probability that 2 females and 1 male will be in a group? C) What is a probability of 3 females only? D) What is a probabilty at least 2

Six Probability Problems

1) In a survey of 125 college students, it was found that of three newspapers, the Wall Street Journal, New York Times, and Chicago Tribune: 60 read the Chicago Tribune 40 read the New York Times 15 read the Wall Street Journal 25 read the Chicago Tribune and New York Times 8 read the New York Times and Wall Street Journa

Probability : Proportion Distribution Problem

Airline company officials find that 86% of all people who make reservations show up for their flights. If an airline has accepted 240 reservations and if there are 213 available seats, find the probability that the airline will have a seat for each person who has reserved one and who shows up.

Probabilities : Strong Law of Large Numbers

Please see the attached file for full problem description. Recall that the sequence of random variables defined on the probability space converges near-certainly towards c if and only if converges towards c) = 1. The purpose of this exercise is to prove the following result: Strong law of large numbers: Let

Probabilities : Probability Density and Marginal Density

Please see the attached file for full problem description. --- The random vector (X,Y) has density.... where is the indicating function on that interval, i.e. it is equal to 1 if y belongs to and is equal to 0 otherwise. a. Evaluate c so that g is a probability density. b. Find the marginal densities of X and Y.

Probabilities : Marginals

A bag contains r balls, of which 2 are red and r - 2 are black. We draw a ball at random, we write down its color, and we put it to one side (not back in the bag). We repeat the procedure r times. Let X be the number of draws needed to obtain a red ball, and let Y be the number of draws needed to obtain a second red ball. a. F

Probability : Exponential Density Function

#26 Please see the attached file for full problem description. a) A lamp has two bulbs of a type with an average lifetime of 1000 hours. Assuming that we can model the probbility of failure of these bulbs by an exponential density function with mean mu = 1000. Find the probability that both of the bulbs fail in 1000 hours.


An octahedron is a three dimensional shape with eight sides that are equilateral triangles. THis shape is used as a die in games such as Dungeons and Dragons because all eight sides come up with equal probability. A. Assuming the sides are numbered 1 through 8, and a person throws two octahedral dice, what are the possible su

Policy Iteration : Probability Distribution and Maximizing Profit

Please see the attached file for the fully formatted problems. 1. A machine in excellent condition earns $100 profit per week, a machine in good condition earns $70 per week, and a machine in poor condition earns $20 per week. At the beginning of any week a machine can be sent out for repairs at a cost of $90. A machine s

Multivariate Probability Distributions

Please see the attached file for the fully formatted problems. Y1 & Y2 denotes the proportions of time that employee I and II actually spent working on their assigned tasks during a workday. The joint density of Y1 & Y2 is given by: f(y1,y2) = y1 + y2 , 0=<y1=<1 , 0=<y2=<1 f(y1,y2) = 0, elsewhere Employee I h


Carol and David decide to play a game as follows: Carol draws and keeps a card from a shuffled pack number 1 to 6. David the draws a card from the remaining 5. The winner is the one holding the card with the highest number. a) Determine whether or not there is an advantage to drawing the first. If the rules are no


FULL WORKINGS PLEASE. Clair and Helen frequently play each other in a series of games of table tennis. Records of the outcomes of these games show that whenever they play a series of games, Clair has a probability 0.6 of winning the first game and that in every subsequent game in the series, Clair's probability of winning the


Show that the probability that exactly one of the events A and B occurs is (see attached).

Probability Based on Random Selection

There are three boxes, each with two drawers. Box I has a gold coin in each drawer Box II has a silver coin in each drawer Box III has a gold coin in one drawer and a silver coin in the other. One box is chosen at random and a drawer is opened from that box. If it contains a gold coin, find the probability that it is in

Probability Based on Order and Random Selection

Four couples, each consisting of one man and one woman, are seated at a circular table. Assuming that each different order is equally likely, find the probability that: a) Andrew is sitting next to his partner b) Benjamin, Charles and David are sitting together (in any order) c) The men and women sit alternately


Please could I have the answer to this: Full workings please. A shortlist of 10 people is drawn up from a large number of applicants for a certain job. The shortlist consists of 7 men and 3 women. Because all the shortlisted applicants are considered to be equally qualified, the names of two of them are drawnn, one afte

Using probability with standard deviation

A particular type of electronic component for use in PCs is mass produced and subject to quality control checks since it is known that 2% of all components produced in this way are defective. The quality of a day's output is monitored as follows. A sample of 10 components is drawn from the day's output (which may be assumed to

Probabilities : Darts on a Dartboard

My uncle plays darts on a circular dart board of radius 20 cm. He assumes a dart lands anywhere on the board with equal probability. a) What is the probability that his dart lands less than 5 cm from the centre of the board? b) That his dart lands exactly 5 cm from the centre? c) My uncle wants to divide his board into ten

Probability : Bracket (Cup) System

Q. The 'cup' system for determining the champion amongst 2^n players consists of drawing lots to arrange the players in 2^n-1 pairs who are to play each other, then repeating this with the 2^n-1 winners of these matches, and so on. The winner and loser of the final match recieve the first and second prizes repectively. Suppose

An Absorbing States Problem

A mouse, after being placed in one of 4 rooms, will search for cheese in that room. If unsuccessful, after one minute it will exit to another room by selecting a door at random. (All the rooms connect to each other.) A mouse entering the room with the cheese will remain in that room. If the mouse begins in room 3, what is the pr

Probability: Birthdays on the Same Day

Determine the number of people needed to ensure that the probability at least two of them have the same day of the year as their birthday is at least 70 percent, at least 80 percent, at 90 percent, 95 percent, at least 98 percent, and at least 99 percent.