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# Probability

### Probability Using Cards

Question: Suppose we turn over cards simultaneously from two well shuffled decks of ordinary playing cards. We say we obtain an exact match on a particular turn if the same card appears from each deck: for example, the queen of spades against the queen of spades. Let pm equal the probability of at least one exact match. Show

### Production & Operation Management

CASE: Mrs. Jones, a robust 50 year old insurance adjuster living in the northern suburbs of Chicago has been diagnosed by a University cardiologist as having a defective heart valve. Although she is otherwise healthy, Jones's heart problem could prove fatal if left untreated. Firm research data are not yet available to predict

### Calculating probability of stock

Let X be the number of gallons of ice cream that is requested at a certain store on a hot summer day. Assume that f(x)= 12x(1000-x)^2/10^12, 0<x<1000, zero elsewhere, is the pdf of X. How many gallons of ice cream should the store have on hand each of these days, so that the probability of exhausting its supply on a particular

### Find the Probability of Rolling a Six

Cast a die a number of independent times until a six appears on the up side of the die. Find the probability density function F(x)= P(X<= x).

### Point Estimation in Statistics

20. A random sample of n bike helmets manufactured by a certain company is selecrted. Let X = the number abong n that are flawed ... a. Derive the maximum likelihood estimator ... b. Is the estimator unbiased? c. If n = 20 and x - 3, what is the mle of the probability ... (see attachment for complete question)

### The Maximum Likelihood Estimator and Bias

20. A random sample of n bike helmets manufactured by a certain company is selected. Let X = the number among the n that are flawed, and let p = P(flawed). Assume that only X is observed, rather than the sequence of S's and F's. a. Derive the maximum likelihood estimator of p. If n = 20 and x = 3, what is the estimate? b. Is t

### Joint Distribution Table : Compute the expected revenue.

26. Consider a small ferry that can accommodate cars and buses. The toll for cars is \$3, and the toll for buses is \$10. Let X and Y denote the number of cars and buses, respectively, carried on a single trip. Suppose the joint distribution of X and Y is as given in the table in Exercise 7 (see attachment). Compute the expected r

### Distribution Function and Pdf

Let X have the pdf f(x)=2x if 0<x<1, zero elsewhere. Let Y=-2 ln X. Find the distribution function and pdf of Y.

### Probability of independent events

If A and B are two independent events with probabilities, P(A)=0.6 and P(B)=0.4, then compute the probability that: (i) Exactly one of them will occur. (ii) Either A or B will occur.

### Probability of Exactly 0 Errors on Ranomly Selected Page ...

a. A book of 450 pages contains 450 random misprint error(s). What is the probability of exactly 0 errors on a randomly selected page? b. What is the probability of at least 3 error(s) on any one page? c. What is the probability of between 1 and 4 (inclusive) random misprint error on any one page? Express you answer using 3 s

### Probability Drawing Three Random White Balls From Bag

A bag contains 5 white, 7 black and 4 red balls, find the chance that three balls drawn at random are white balls.

### System of Components Connected

78. Consider the system of components connected as in the accompanying picture... Please see attached.

### Biostatistics - Survival Rates

1.Go to this WHO website: http://www3.who.int/whosis/life/life_tables/life_tables.cfm?path=whosis,life,life_tables&language=english Look up the life table for Afghanistan. A.Plot the survival curve for males and for females. Briefly describe any differences or trends. B.What is the chance of surviving birth to age 60 f

### Probability: Randomly Selecting Marbles

I need you to explain to me step by step how to solve this problem. I am having trouble understanding this question. Question: A bag contains 40 blue marbles, 40 red marbles, and 20 green marbles. 60 of the marbles are big. These marbles are selected at random without replacement. What is the probability of randomly selecti

### Mean Household Size and Roulette Probability

It's estimated that 57% of Americans live in households with 1 or 2 people, 32% live in households with 3 or 4 people and 11% live in households with 5 or more. Explain how you will find the expected number of people in an American household. The probability of winning when you bet on a single number in roulette is 1 in 3

### Probability, Density Function and Random Variable

Check that {see attachment} is a density function. Please see attachment for complete list of questions.

### Probability Distribution

Shaquille O'Neal is not recognized as good free throw shooter. Career average is 0.532 (53.2%). Suppose in a game Shaq takes 5 free throws. a. What type of probability distribution is this? Explain (Binomial???) b. What are the mean and standard deviation for the number of made free throws? c. What is the probability

### 2 Statistics Problems

1) One of the ways most Americans relieve stress is to reward themselves with sweets. According to one study, 46% admit to overeating sweet foods when stressed. Suppose that the 46% figure is correct and that a random sample of n = 100 Americans is selected. a) Does the distribution of p^, the sample proportion of Americans w

### For what value of c is f(x)... a density function?

For what value of c is f(x)... a density function? Please see attached for full question.

### Mean/Variance of Random Variables Having Gamma/Beta Distribution

Find the mean and variance of random variables having the Gamma and Beta distributions, described in Definitions 3.11 and 3.12. Please see the attached file for full question.

### Probability

The Northside Rifle team has two marksperson, Dick and Sally. Dick hits a bull's-eye 90% of the time, and Sally hits a bull's-eye 95% of the time. (a) What is the probability that either Dick or Sally or both will hit the bull's-eye if each takes one shot? (b) What is the probability that Dick and Sally with both hit the bull'

### Posterior probability. What is the posterior probability that the lathe tool is properly adjusted?

Ace Machine Works estimates that the probability its lathe tool is properly adjusted is 0.8. When the lathe is properly adjusted, there is a 0.9 probability that the parts produced pass inspection. If the lathe is out of adjustment, however, the probability of a good part being produced is only 0.2. A part randomly chosen is ins

### Probability and Statsitcs (SMOG and FOG tests)

I am a mature student (age 60) currently working for a training company. I have been asked to complete a training project which involves these questions and have already done some of the work; however, I need to confirm my answers for these last few questions. I have attached the questions along with the SMOG and FOG data she

### Probability Distribution

Give a probability distribution for the following: In 1992, the Big 10 collegiate sports conference moved to have women compose at least 40% of its athletes within 5 years. Suppose they exactly achieve the 40% figure, and that 5 athletes are picked at random from Big 10 universities. The number of women is recorded. For th

### Exponential Class of Distributions

7.5.3 Let X1, X2,..,Xn denote a random sample of size n from a distribution with pdf f(x; è) =èx^(è-1), 0<x<1, 0 elsewhere, and è>0. Show that the geometric mean (X1X2...Xn)^(1/n) of the sample is a complete sufficeint statistic for è. Find the maximum likelihood estimator and observe that it is a function of this geome

### Probability of selecting a dog

If a person adopts a pet there is a 45% it'll be a cat and 55% it will be a dog (a local dog and cat adoption). If a cat is adopted there is 60% chance it will be a female. If a dog is adopted there is 35% chance it is a female. A random selection is made and it was a male. What is the the probability that the selection is a

### Uniform and Exponential Distributions

A) A fire station is to be located along a road of length A, A<&#8734;. If fires will occur at points uniformly chosen of (0, A), where should the station be located so as to minimize the expected distance from the fire? That is, choose a so as to minimize E[|X-a|] when X is uniformly distributed over (0,A). b) N

### Simple Statistics: Probability for Standard Normal Random Variable

6.3. Find the following probabilities for the standard normal random variable z: {see attachment} 6.7. Find a Zo that has area .9505 to its left. Find a Zo that has area .05 to its left.

### Finite math/business analysis Multiple choice - normal distribution, probability distribution and Central Limit Theorem

If a particular batch of data is approximately normally distributed, we would find that approximately: a. 2 of every 3 observations would fall between ±1 standard deviation around the mean. b. 4 of every 5 observations would fall between ±1.28 standard deviations around the mean. c. 19 of every 20 observations would fall be

### Probability Questions

A professor grades homework by randomly choosing 5 out of 12 homework problems to grade. a) How many different groups of 5 are there from the 12 problems? b) Jerry did only 5 problems of one assignment. What is the probability that the problems he did comprised the group that was selected to be graded? c) Silvia did 7 pro