(-10)( .225) + (0)( .0375 ) + (10)( .4875 ) = -3 + 0 + 6.5 = 3.5 .75 .75 .75 2. (S & W 2.18) (a) The mean of is (Note that this is the population mean) The variance of is so the standard deviation of Y is (b) (i) the sample mean. Since Yi is an i.i.d. random variable, the expected value of Y bar is equal to the population mean from part (a). (ii) First calculate the variance: The, using the
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amusement park and calculate the relative frequency for the shortest distance. (Points : 4) .375 .150 .500 .300 .333 | 2. The following is a relative frequency distribution of grades in an introductory statistics course. If this was the distribution of 200 students, find the frequency of failures: (Points : 4) 12 6 23 46 3 | 3. A random sample of 12 joggers was asked to keep track and report the number
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The estimate β is usually accompanied by a standard error ˆ to indicate how precisely it is estimated. We denote this standard error as se(β). This ˆ is a random variable with a sampling distribution. It will have reflects the fact the β different values in different samples. We can then form the following test statistic by computing the standardised statistic ˆ whereby we subtract the hypothesisized value β0 from the estimate β and divide by its standard error: t-stat = ˆ β − β0 ˆ se(β) ˆ Again
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score that occurs most frequently. Median = middle score when scores are ranked in order. Mean = the average score, the media. Interpreting the standard deviation: -the empirical rule (frequency distribution is bell shaped and symmetric) 68% values: -1 - +1 95% values: -1 - +1 99.7 % values: -3 - +3 -Chebyshev’s rule (applies to all distributions, regardless their shape) ?% values: -1 - +1 75% values: -2 - +2 88.9% values: -3 - +3 o Choice of numerical measures depends
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Online Reference & Tools Home>Math>Math symbols> Math symbols Mathematical Symbols List of all mathematical symbols and signs - meaning and examples. Basic math symbols Geometry symbols Algebra symbols Probability & statistics symbols Set theory symbols Logic symbols Calculus & analysis symbols Number symbols Greek symbols Roman numerals Basic math symbols Symbol Symbol Name Meaning / definition Example = equals sign equality 5 = 2+3 ≠ not equal sign inequality 5 ≠ 4 > strict inequality
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to generate. 1. Continuous distributions: Generate and store in column c1 10,000 values from the uniform distribution on the interval [3,7] as follows: random 10000 c1; uniform 3 7. [3] a. Use mean command to find the sample mean x of these data———————– ¯ [2] b. What is the mean µ of the uniform distribution on the interval [3,7]?————[1] c. Compare µ to the value x you found in part a). ———————– ¯ Generate and store in column c2 1,000 values from exponential distribution with parameter λ = .125 as
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A) = 1; P(A) = 1- P(not A); P(At least one) = 1 – P(none) ……………………………………………………………………………………………………………………………………………………………………… ……………………………………………………………………………. 1)UNIFORM DISTRIBUTION: The area under the uniform distribution: P( Mx1 ) z1= 1 - CI% x% (confidence interval dat) of the observation fall below X 3) BINOMIAL DISTRIBUTION: calculez : p(success); n= total no; x = number of successes in sample- ni se da in intrebare; BINOMIAL FORMULA: p(x)= [n!/ (X! (n-x)!)]*px(1-p)n-x ; P(x=x) =P(1)+
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Temperature, and Low Temperature. List the past 60 days for which data is available. 2. Prepare a histogram for the data on high temperatures and comment on the shape of the distribution as observed from these graphs. 3. Calculate and S. mean 40.7483 Standard deviation 1.905878 4. What percentage of the high temperatures are within the interval – S to + S? 38.842452 to 42.654208 48/60=.8 or 80%
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For Students Solutions to Odd-Numbered End-of-Chapter Exercises * Chapter 2 Review of Probability 2.1. (a) Probability distribution function for Y Outcome (number of heads) | Y 0 | Y 1 | Y 2 | Probability | 0.25 | 0.50 | 0.25 | (b) Cumulative probability distribution function for Y Outcome (number of heads) | Y 0 | 0 Y 1 | 1 Y 2 | Y 2 | Probability | 0 | 0.25 | 0.75 | 1.0 | (c) . Using Key Concept 2.3: and so that 2.3. For the two new random
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rather than a z-test. It is always good to perform the standard exploratory data analysis before commencing any hypothesis testing involving t-tests. It is often useful to check through summary statistics (like the minimum and maximum of the data), as well as a quick plot of the data (box-plots), to check for any problematic data or outliers. The use of a t-test requires the assumption that the data is distributed like a normal distribution – essentially a bell-shaped curve for the histogram. Therefore
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