MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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P(x) 0.16 0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00 6 8 10 12 14 o² = Var(x) = Σ x² · P(x) − µ² 16 The probability histogram above is for successes out of a sample of size n = 20. The probabilities that n is 0, 1, 2, 18, 19, or 20, are each so low that they do not even show up as bars on the graph. But there is a measurable probability for each that is just very small. Any discrete probability distribution table can be converted to a histogram. μ = E(x) = [x · P(x) 3 18 We can use these histograms to check for skewdness and bell-curve shapes as in earlier chapters. Whenever the distribution is symmetric and bell-curves, then it is possible and useful to compute the mean, standard deviation, and variance of a random variable. We do this using the probability distribution. The mean of the random variable is a population mean since it comes from exact probabilities, and not from sample data. Thus it is often called an expected value. DEFINITION: Mean, Variance, and Standard Deviation of a Discrete Probability Distribution 20 J = x √Σx² x². P(x) - μ²
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Transcribed Image Text:P(x) 0.16 0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00 6 8 10 12 14 o² = Var(x) = Σ x² · P(x) − µ² 16 The probability histogram above is for successes out of a sample of size n = 20. The probabilities that n is 0, 1, 2, 18, 19, or 20, are each so low that they do not even show up as bars on the graph. But there is a measurable probability for each that is just very small. Any discrete probability distribution table can be converted to a histogram. μ = E(x) = [x · P(x) 3 18 We can use these histograms to check for skewdness and bell-curve shapes as in earlier chapters. Whenever the distribution is symmetric and bell-curves, then it is possible and useful to compute the mean, standard deviation, and variance of a random variable. We do this using the probability distribution. The mean of the random variable is a population mean since it comes from exact probabilities, and not from sample data. Thus it is often called an expected value. DEFINITION: Mean, Variance, and Standard Deviation of a Discrete Probability Distribution 20 J = x √Σx² x². P(x) - μ²
6. On page 3 of chapter 4 there is a discrete probability histogram. On this graph, what are the exact values that count as the edges for the discrete random variable x = 10? O The bar is from 9.8 to 10.2 O The bar is from 9.5 to 10.5. O The bar is from 10 to 11. The bar is from 9 to 10.
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Transcribed Image Text:6. On page 3 of chapter 4 there is a discrete probability histogram. On this graph, what are the exact values that count as the edges for the discrete random variable x = 10? O The bar is from 9.8 to 10.2 O The bar is from 9.5 to 10.5. O The bar is from 10 to 11. The bar is from 9 to 10.
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