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22 Cards in this Set
- Front
- Back
Mean is a measure of location, but median is a measure of variability.
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F median is a measure of location
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A Poisson random variable is continuous because it can take an infinite number of values.
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F Poisson random variable is no continuous. it is discrete
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The number of vehicles passing an intersection during a 15-minute period can be described
by a Bernoulli random variable |
F
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If X follows a normal distribution N(u,o^2) with a pdf of f(x) = 1/sqrt(2pi*o) * e^(-(x-u)^2/(2o^2)/(2o^2)) then both Z = (X-u)/o and Z'= -(X-u)/o follow a standard normal distribution
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T
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For n random variables defined for the same population, X1, X2,...,Xn, then V(a1X1+a2X2+,"",,+anXn) = a1^2V(X1) + a2^2V(X2) + ... +an^2V(Xn) is correct whether these random variables are independent or not
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F. random variables must be independent
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For a simple random sample size n>30, X1, X2, ..., Xn, from a population of uniform distribution, the samplem an could follow a uniform distribution
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F. normal distribution
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The Central Limit Theorem states that, for a large sample size (e.g. n>30) we have E(X\bar) = u and V(X\bar) = o^2/n, where u and o^2 are population mean and variance, respectively
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F. CLT shows type of distribution, not location or variablity
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For a simple random sample of size n, X1, X2, ... , Xn, u\hat = (X1+X2)/2 is an unbiased estimator of the population mean
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T
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If the size of a simple random sample is very large, n>30, then an unbiased estimator of the population mean will equal the population mean
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F
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For a population, which follows a uniform distribution with a known standard deviation o, we denote x\bar as a sample mean of size n> 30. For 95% of the time, the population mean lies in [x\bar - 1.96o/sqrt(n) , x\bar - 1.96o/sqrt(n)]
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F
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With a larger sample size, we can obtain a narrower confidence interval of population mean for the same confidence level
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T
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In hypotheses tests, type I errors occur when the null hypotheses is wrong but we accept it
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F. type I error is rejection null hypothesis when it is correct. described is type II error
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In hypothesis tests, the significance level is defined as the probability of making type I errors
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T
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For alternative hypothesis, Ha: u > uo the rejection region should be X\bar > d with d > uo
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T
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If we can reject a null hypothesis at the significance level of 5% then we can reject it at the significance level of 10%
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T. higher significance level = wider range = less precision
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The random number of cars passing an intersection during 15 minutes can be described by a uniform distribution
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F. discrete numbers
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The time difference between two successive vehicles can be described by a Bernoulli random variable
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F. bernoulli only offers 0 and 1
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For a continuous random variable X, P(X=a) = 0 for any number a
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T
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For a continuous random variable X, the pdf f(x) can be greater than 1 but the cdf F(x) can never be greater than 1
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T
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For a standard normal random variable Z, if the ara under the pdf to the right of za is a, then P(Z>=za) = a
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T
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For n random variables defined for the same population, X1, X2,...,Xn, then E(a1X1 + a2X2 + ... + anXn) = a1E1(X1) + a2E2(X2) + ... + anEn(Xn) is correct whether these random variables are independent or not
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T
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For a simple random sample of size n, X1, X2, ... , Xn, from a population of Bernoulli distribution, the sample mean could follow a Bernoulli distribution
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F. the RANDOM sample mean could follow a NORMAL distribution
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