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1. The random vector (X, Y )t has a two-dimensional normal distribution with Var X = Var Y . Show that X + Y and X - Y are independent random variables.
2. Suppose that X and Y have a joint normal distribution with E X = E Y = 0, Var X = σ2 , Var Y = σ2, and correlation coefficient ρ. Compute E XY x y and Var XY.
Remark. One may use the fact that X and a suitable linear combination of X and Y are independent.
If S exists, then S(x, y) = 0 ∈ R. Then by Problem 4 there must be neighborhoods U of x and V of y in K such that S(u, v) ∈ R and |S(u, v)| 1 for all u ∈ U and v ∈ V . Show, however, that each of U and V contains real numbers of arbitrarily l..
Test the data for normality. If the data are not normal, try a suitable transformation to make the transformed data approximately normal.
using a 5 level of significance and a sample size of 26 what is the critical value for a one-tailed hypothesis
Number of rescue calls received by rescue squad in city follows a Poisson distribution with mu = 2.83 per day. Squad can handle at most four calls a day. Determine the probability that squad will be able to handle all calls on a particular day?
siegal found that elderly people who owned dogs were less likely to visit the doctor after upsetting events than were
The speeds of all vehicles have a bell-shaped distribution with a mean of 72 mph and a standard deviation of 3 mph. Using the empirical rule, find the percentage of vehicles with the following speeds on this section of I-95.
Is the mean list price of a house lower if there are 3 bedrooms compared to 4 bedrooms? To answer this question we will construct a confidence interval and hypothesis test.
Sampling distributions. Given a normal distribution with μ = 50 and standard deviation σ = 9, if a sample of n = 100 is selected.
A small independent stock broker has created four sector portfolios for her clients. Each portfolio always has five stocks that may change from year to year The volatility (coefficient of variation) of each stock is recorded for each year.
scores on a standardized test are normally distributed with a mean of 100 and a standard deviation of 12. an
use hypothesis testing to test the independence of opinion between the two groupsprefer lecture prefer computer
Scrap rates per thousand (parts whose defects cannot be reworked) are compared for 5 randomly selected days at three plants. Does the data prove a significant difference in mean scrap rates?
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