Suppose X and Y have joint probability density function [C(x²+y²), _if0
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a) What is the value of C.
b) What is the variance of X.
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- We are interested in determining whether or not the variances of the sales at two music stores (A and B) are equal. A sample of 16 days of sales at store A has a sample variance of 20 while a sample of 26 days of sales from store B has a sample variance of 30. The test statistic isTRUE OR FALSE Answer numbers 8-10Assume a variable has only 3 observations: x1=1, x2=5, x3=6. What is the variance of this variable x? 8.6 None of others. 4.7 2.9
- How many F ratios are figured in a two-way analysis of variance? 1 2 3 as many as there are cells in the designFind the variance of the dataActuaries use various parameters when evaluating the cost of a life insurance policy. The variance of the life spans of a population is one of the parameters used for the evaluation. Each year, the actuaries at a particular insurance company randomly sample 30 people who died during the year (with the samples chosen independently from year to year) to see whether the variance of life spans has changed. The life span data from this year and from last year are summarized below. Current Last Year Year x1 = 75.8 | x,= 76.2 si= 47.61 s3= = 92.16 (The first row gives the sample means and the second row gives the sample variances.) Assume that life spans are approximately normally distributed for each of the populations of people who died this year and people who died last year. Can we conclude, at the 0.05 significance level, that the variance of the life span for the current year, of, differs from the variance of the life span for last year, o,? Perform a two-tailed test. Then complete the…
- Let X₁, X2,..., be a sequence of independent and identically distributed random variables, each with a mean value x and variance ok, both of which are assumed to be finite. Let N be a discrete random variable independent of X₁, X2,..., and assuming values in the set {0, 1, 2, ...}, with mean value N and variance ok (both are finite). Form the random-compound sum Y=1 Xk, with the convention Y = 0 whenever N = 0.Assume that we have a data set composed of three features. After doing PCA we find that the variances of the three principal components are 18, 5 and 1. What fraction of the variance of all the data can be expressed in terms of the first principal component? Select one: О а. 7/8 b. 2/3 O C. All of it. O d. 3/4Once the correlation coefficient is known, how can we find the amount of the shared variance?