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A random variable can assign a different number to each possible outcome. |
2. |
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A random variable must assign a different number to each possible outcome. |
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The sum of all the probabilities P(X=x) for all possible values of x must equal 1. |
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The histogram of X will be highest at the expected value of X. |
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The expected value of X is half-way between the largest and smallest possible values of X. |
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The sample means approach the population mean as the sample size gets larger and larger. |
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If is the expected value of X, then the expected value of X- = 0. |
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If is the expected value of X, and x1, x2, . . ., xn is a sample of values of X, then (x1 + x2 + . . . + xn) / n = . |
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If is the expected value of X, and x1, x2, . . ., xn is a sample of values of X, then (x1 + x2 + . . . + xn)/n should be close to if n is large. |
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If a coin is tossed five times, then the probability of heads coming up twice is the same as the probability of heads coming up three times. |
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If heads has come up six times in a row, then tails is more likely to come up on the seventh toss. |
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I If you toss a coin seven times, is more likely that heads will come up six times and tails once than that heads will come up seven times in a row. |
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In a sequence of n independent Bernoulli trials, with a probability p of success in each, we expect to get about np successes. |
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We should expect the actual values of X obtained in experiments to be within one standard deviation away from the mean. |
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If is the expected value of X, and X has a symmetric, bell-shaped distrtibution, then Chebyschev's rule does not apply. |
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If is the expected value of X and is the standard deviation, we should expect the average of (X -)2 to be 2. |
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For any X, approximately 68% of its values obtained in a sample will lie within one standard deviation of its mean. |
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For a normal X, approximately 68% of its values obtained in a sample will lie within one standard deviation of its mean.. |
19. |
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For any X, at least 3/4 of its values obtained in experiments will lie within 2 standard deviations of its mean. |
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For a normal X, at least 95% of its values obtained in experiments will lie within 2 standard deviations of its mean. |
21. |
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For any X, at least 88% of its values obtained in experiments will lie within 3 standard deviations of its mean. |
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For a symmetric and bell-shpaed distribution X, we expect at least 99% of its values obtained in experiments to lie within 3 standard deviations of its mean. |
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A binomial distribution has exactly the same probabilities as a normal distribution. |