STAT-2126EL Lecture 2: Probability

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emeraldzebra745

21 Jan 2017

School

Laurentian

Department

Statistics / Statistique

Course

STAT-2126EL

Professor

Emond Michael

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Document Summary

Defined as the likelihood of a given outcome occurring when several outcomes are possible. Probability of a = number of outcomes of a / total number of possible outcomes. Each individual has an equal choice of being selected. Three must be sampling with replacement to keep the probability of selection consent for each individual. Random sampling is different than random assignment. You can have a random sample and still bias your results by putting only certain individuals in the control or experimental group. So when selecting our subjects we want: Samples that reflect our population of interest. The fact that when there is something that has lots of events, some of them will tend to clump together here and there, purely by chance. With 50 sars death in toronto, people were having some outrageous responses (1000 people die in canada of the flu every year. ) Ad advertisement for miller brewing company once ran:

Related Questions

People enter a restaurant and check their hat at the coat check, but since the worker is new, he makes the mistake of throwing all the hats in a pile. When the patrons return to claim their hats at the end of the evening, the worker gives each person a random hat from the pile.

1. What is the probability that no one receives their own hat back if there are only 2guests?

2. What is the probability that no one receives their own hat back if there are 3 guests?

3. What is the probability that no one receives their own hat back if there are 4 guests?

4. What is the probability that no one receives their own hat back if there are 8 guests?

5.What is the probability that no one receives their own hat back if there are 10 guests?

To solve, build a systematic method. For example, one way you could do it is by defining several events, where P_i = the number of ways of a person i to recive their hat correctly, and then the number of ways that at least one person to recive their hat is the union of P_1,...,P_n; finally, you can count this using inclusion/exlusion, then count the complement to finish the problem.

brownbeetle44

The migration pattern of Monarch butterflies are tracked by a catch-and-release method in which individual butterflies are tagged with a circular, lightweight sticker placed carefully on the wings so as not to impede their ability to fly. The sticker contains a unique ID number. Volunteers across the U.S. and South America capture the butterflies, record the IDs if they are tagged, and release them. This allows us to track the locations each unique ID is found, allowing us to estimate the migration pattern. On average, 1 out of 100 captured butterflies are already tagged. Suppose you are a volunteer and capture 50 butterflies; let $X$ denote the number of those that are already tagged. What is the distribution of $X ?$ What is the probability that you catch at least one tagged butterfly?

greyskunk455

Consider the following sample of observations on coating thickness for low-viscosity paint. ("Achieving a Target Value for a Manufacturing Process: A Case Study," J. of Quality Technology, 1992:22-26):

0.83	0.88	0.88	1.04	1.09	1.12	1.29	1.31
1.48	1.49	1.59	1.62	1.65	1.71	1.76	1.83

Assume that the distribution of coating thickness is normal (a normal probability plot strongly supports this assumption).

(a) Calculate a point estimate of the mean value of coating thickness, and state which estimator you used.

(b) Calculate a point estimate of the median of the coating thickness distribution, and state which estimator you used.

(c) Calculate a point estimate of the value that separates the largest 10% of all values in the thickness distribution from the remaining 90% and state which estimator you used. [Hint: Express what you are trying to estimate in terms of m and s]

(d) Estimate P(X<1.5), i.e., the proportion of all thickness values less than 1.5 [Hint: if you know the values of and , you could calculate this probability. These values are not available , but they can be estimated.]

(e) What is the estimated standard error of the estimator that you used in part (b)?

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STAT-2126EL Lecture 2: Probability

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