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1. Suppose that on each play of the game a gambler either wins 1 with probability p or loses 1 with probability 1 - p. The gambler continues betting until she or he is either up n or down m. What is the probability that the gambler quits a winner?
2. A particle moves among n + 1 vertices that are situated on a circle in the following manner. At each step it moves one step either in the clockwise direction with prob- ability p or the counterclockwise direction with probability q = 1 - p. Starting at a speci?ed state, call it state 0, let T be the time of the ?rst return to state 0. Find the probability that all states have been visited by time T.
Compare the flows in the three lanes by making parallel boxplots. Which lane typically serves the most traffic? Examine the relationships of the flows in the three lanes by making scatterplots. Can you explain the patterns you see
determine the sample size needed to construct a 90 confidence interval to estimate the population mean when ? 75 and
Use 0.01 significance level to test the claim that the selection process is biased against Mexican-Americans. What is the mean and standard deviation for the numbers of Mexican Americans?
the student government association at southwestern state university wanted to demonstrate the relationship between the
discuss the following statements and explain why they are true or falsea increasing the number of predictor variables
The demand, D, on any given day is uniformly distributed over [80,140]. How many units should the retailer order to maximize expected profit?
from 1975 to 1986 the general social survey asked its participants if they favored or opposed capital punishment. a
the u.s. dairy industry wants to estimate the mean yearly milk consumption. a sample of 17 people reveals the mean
what are binary variables and when would it be necessary to use binary variables in an optimization problem? give a
the density function for a series of processes is fx x 32x2 for ?1 lt x lt 1. choose 10 numbers independently from
The scores, X, of an examination may be assumed to be normally distributed with μ = 70 and σ2 = 49. What is the probability that:
In a study of how managers attempt to manage earnings, researchers analyzed a sample of 515 earnings- management attempts from a survey of experienced auditors. The frequency of effects is summarized in the table shown. Research question: At α..
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