Explanation Formula used: The mean and standard deviation for the continuous random variable are, (1) Mean μ = ∫ − ∞ ∞ x f ( x ) d x . (2) Standard deviation σ = V ( X ) , where variance V ( X ) = ∫ − ∞ ∞ x 2 f ( x ) d x − μ 2 . Calculation: The probability density function is f ( x ) = { p x p + 1 if x ≥ 1 0 otherwise . By using the above formula, compute the mean with respective probability density function. μ = ∫ − ∞ 1 p x p + 1 x d x + ∫ 1 ∞ p x p + 1 x d x = 0 + p lim b → ∞ ∫ 1 b x − p d x = p lim b → ∞ [ x − p + 1 − p + 1 ] 1 b = p 1 − p lim b → ∞ [ ( b ) − p + 1 − ( 1 ) − p + 1 ] On further simplification. μ = p 1 − p [ − 1 ] = p p − 1 Thus, the value of mean is μ = p p − 1 . In order to find the standard deviation, first compute the variance. V ( X ) = ∫ − ∞ ∞ p x p + 1 x 2 d x − ( p p − 1 ) 2 ( ∵ μ = p p − 1 ) <

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Chapter 11.4, Problem 66E

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To find: The standard deviation of a probability density function and explain the restriction on p in standard deviation.

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Chapter 11.4, Problem 65E

Chapter 11.4, Problem 67E

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4. (5 pts) Conduct a chi-square contingency test (test of independence) to assess whether there is an association between the behavior of the elderly person (did not stop to talk, did stop to talk) and their likelihood of falling. Below, please state your null and alternative hypotheses, calculate your expected values and write them in the table, compute the test statistic, test the null by comparing your test statistic to the critical value in Table A (p. 713-714) of your textbook and/or estimating the P-value, and provide your conclusions in written form. Make sure to show your work. Did not stop walking to talk Stopped walking to talk Suffered a fall 12 11 Totals 23 Did not suffer a fall | 2 Totals 35 37 14 46 60 T

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Name: Lab Time: Quiz 7 & 8 (Take Home) - due Wednesday, Feb. 26 Contingency Analysis (Ch. 9) In lab 5, part 3, you will create a mosaic plot and conducted a chi-square contingency test to evaluate whether elderly patients who did not stop walking to talk (vs. those who did stop) were more likely to suffer a fall in the next six months. I have tabulated the data below. Answer the questions below. Please show your calculations on this or a separate sheet. Did not stop walking to talk Stopped walking to talk Totals Suffered a fall Did not suffer a fall Totals 12 11 23 2 35 37 14 14 46 60 Quiz 7: 1. (2 pts) Compute the odds of falling for each group. Compute the odds ratio for those who did not stop walking vs. those who did stop walking. Interpret your result verbally.

Chapter 11 Solutions

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Ch. 11.1 - Evaluate the following, if it converges: 3dx(x1)2.Ch. 11.1 - Prob. 2MP Ch. 11.1 - Prob. 3MP Ch. 11.1 - Prob. 4MP Ch. 11.1 - Prob. 5MP Ch. 11.1 - Prob. 6MP Ch. 11.1 - Prob. 1ED Ch. 11.1 - Prob. 2ED Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E

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