27.12. There can be asymptotic normality even if there are no moments at all. Construct a simple example.

6.21. For two observations 'a' and 'b', show that standard deviation is half the distor between them.

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5. A group of doctors are conducting a clinical trial for an experimental cancer drug. The graph below shows the probability of patient survival as a function of time, t (in months). The functions for Streated (survival probability of patients treated by the drug) and Splacebo (survival probability of patients given a placebo) are determined to be: Streated(t) = e-() and Splacebo (t) = e #. Use the given function (a) Splacebo (t) = e-i to calculate the average survival probability of the placebo group for the first 10 months of the study. Round to 2 decimal places. Ste 0. -0.6 -0:4 -02 10 20 (b) The efficacy of the drug at any time 7 >0 can be defined as E(7) = (Streated(t) – Splacebo (t)) dt. Note: This can be thought of as representing a difference of areas. Use a Riemann sum with 5 sub-intervals of equal width to approximate E(10). Use right endpoints. Round your final answer to 2 decimal places. (c) the first 7 months). Is the drug beneficial at 10 months? (A short one-sentence…

he average American gets a haircut every 41 days. Is the average larger for college students? The data below shows the results of a survey of 16 college students asking them how many days elapse between haircuts. Assume that the distribution of the population is normal. 38, 40, 44, 39, 50, 53, 47, 46, 51, 40, 49, 42, 38, 43, 54, 45 What can be concluded at the the αα = 0.05 level of significance level of significance? The test statistic    Correct =  (please show your answer to 3 decimal places.)   The p-value =  (Please show your answer to 3 decimal places.) The p-value is     αα Based on this, we should      the null hypothesis.

5.1: 13) When estimating distances from a table of velocity data, it is not necessary that the time intervals are equally spaced. After a space ship is launched, the following velocity data is obtained. Use these data to estimate the height above the Earth's surface at 127 seconds. Lower estimate of distance traveled= ? Miles Upper estimate of distance traveled= ? Miles

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Approximate the population mean and standard deviation of age for females. By the way, we find the midpoints by adding the first numbers before the hyphens in the age column and then dividing by 2 (ex: 0+10/2=5, 10+20/2=15, 20+30/2=25).