7-7 Geometric Sequences as Exponential Functions Determine whether each sequence is arithmetic, geometric, or neither. Explain. 1. 200, 40, 8, … SOLUTION: Since the ratios are constant, the sequence is geometric. The common ratio is 2.
Answer: True Difficulty: Medium 7. A minimum variance, unbiased point estimate has a variance that is as small or smaller than the variances of any other unbiased point estimate. Answer: True Difficulty: Medium 8. We can randomly select a sample from an infinite population of potential process measurements by sampling the process at different and equally spaced time points. Answer: True Difficulty: Medium (REF) 9.
ANSWER: a -recall that all the t-values are larger than the z-values so it makes it more difficult to reject the null. 2. Read the t statistic from the table of t distributions and circle the correct answer. A two-tailed test, a sample of 20 at a .20 level of significance; t = a. 1.328 b.
1. The graph approximates the points: E(r) σ Minimum Variance Portfolio 10.89% 19.94% Tangency Portfolio 12.88% 23.34% 10. The reward-to-variability ratio of the optimal CAL (using the tangency portfolio) is: 11. a. The equation for the CAL using the tangency portfolio is: Setting E(rC) equal to 12% yields a standard deviation of: 20.56% b. The mean of the complete portfolio as a function of the proportion invested in the risky portfolio (y) is: E(rC) = (l - y)rf + yE(rP) = rf + y[E(rP) - rf] = 5.5 + y(12.88 - 5.5) Setting E(rC) = 12% ==> y = 0.8808 (88.08% in the risky portfolio) 1 - y = 0.1192 (11.92% in T-bills) From the composition of the optimal risky portfolio: Proportion of stocks in complete portfolio = 0.8808 × 0.6466 = 0.5695 Proportion of bonds in complete portfolio = 0.8808 × 0.3534 = 0.3113 12.
 Precision: measure of how close a series of measurements are to one another.  Accepted Value: the correct value based on reliable references  Experimental Value: the value measured in the lab.  Error: o Error = experimental value – accepted value  Percent error: o Percent Error = |error| x 100% Accepted value  Significant Figures: all of the digits that are known, plus a last digit that is estimated. o
Additional info b). Additional info b. Explanation 2. Point (parenthetical documentation) a. Explanation b.
Quantitative psychological research is where the research findings result from mathematical modeling and statistical estimation or statistical inference. Since qualitative information can be handled as such statistically, the distinction relates to method, rather than the topic studied. There are three main types of psychological research: 1. Correlational research In statistics, dependence is any statistical relationship between two random variables or two sets of data. Correlation refers to any of a broad class of statistical relationships involving dependence.
Assignment #2 1) Improve the result from problem 4 of the previous assignment by showing that for every e> 0, no matter how small, given n real numbers x1,...,xn where each xi is a real number in the interval [0, 1], there exists an algorithm that runs in linear time and that will output a permutation of the numbers, say y1, ...., yn, such that ∑ ni=2 |yi - yi-1| < 1 + e. (Hint: use buckets of size smaller than 1/n; you might also need the solution to problem 3 from the first assignment!) 2) To evaluate FFT(a0,a1,a2,a3,a4,a5,a6,a7) we apply recursively FFT and obtain FFT( a0,a2,a4,a6) and FFT(a1,a3,a5,a7). Proceeding further with recursion, we obtain FFT(a0,a4) and FFT(a2,a6) as well as FFT(a1,a5) and FFT(a3,a7). Thus, from bottom up, FFT(a0,a1,a2,a3,a4,a5,a6,a7)
Expectation and variance of a random variable Let be a random variable with the following probability distribution: Value of | | 20 | 0.10 | 30 | 0.35 | 40 | 0.30 | 50 | 0.10 | 60 | 0.15 | Find the expectation and variance of . In this question, the random variable takes on the values , , , , and , with respective probabilities , , , , and . Thus, we have | | | | | | | | | The variance of a discrete random variable is the weighted mean of the squared deviations of the possible values of from their mean: | =(20-38.5) sec pow(0.10)+(30-38.5)sec pow(0.35)+(40-38.5)sec pow(0.30)+(50-38.5)sec pow(0.10)+(60-38.5)secpow(0.15) Var(X)= 142.75 ------------------------------------------------------------------------------------------------------------- Binomial problems: Mean and standard deviation A rainstorm in Portland, Oregon, wiped out the electricity in of the households in the city. Suppose that a random sample of Portland households is taken after the
Benford's Law Benford's law, also called the First-Digit Law, refers to the frequency distribution of digits in many (but not all) real-life sources of data. In this distribution, 1 occurs as the leading digit about 30% of the time, while larger digits occur in that position less frequently: 9 as the first digit less than 5% of the time. Benford's law also concerns the expected distribution for digits beyond the first, which approach a uniform distribution. It has been shown that this result applies to a wide variety of data sets, including electricity bills, street addresses, stock prices, population numbers, death rates, lengths of rivers, physical and mathematical constants,and processes described by power laws (which are very common in nature). It tends to be most accurate when values are distributed across multiple orders of magnitude.