If Var(X1) = 2, Var(X2) = 4, Var(X3) = 3, Cov(X1, X2) = 1, Cov(X1, X3) = -2, and X2 and X3 are independent, find the mean and variance of Y = X1 – 2X2 +3X3.
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- how to (w^1) get distributed back into (y+q^1)?Make sure to show the correct work and solution: Prove ρ ≤ 1 if ρ is the correlation of X and Y .Suppose that in a certain chemical process the reaction time (in hours) is related to the temperature (°F) in the chamber in which the reaction takes place, according to the simple linear regression model where β0 = 5.23, β1 = -0.01, and σ = 0.09. If the temperature is 260°F, what is the probability that the reaction time is between 2.51 and 2.7 hours? Suppose five observations are made independently on reaction time, each one for a temperature of 260°F. What is the probability that all five times are between 2.51 and 2.7 hours? If two independently observed reaction times for temperatures are 1° apart, what is the probability that the time at the higher temperature exceeds the time at the lower temperature?
- John Swanson, president of Market Research Inc., has asked you to estimate the coefficients of the modelY = β0 + β1X1 + β2X21 + b3X2where Y is the expected sales of office supplies for a large retail distributor of office supplies, X1 is the total disposable income of residents within 5 miles of the store, and X2 is the total number of persons employed in information-based businesses within 5 miles of the store. Recent work by a national consulting firm has concluded that the coefficients in the model must have the following restriction:b1 + b2 = 2Describe how you would estimate the model coefficients using least squares.If two variables are related so that increasing values of one variable are associated with decreasing values of other, then there is a what relationship between the varialves?Show that (X+1)/(n+2) is a biased estimator of the binomial parameter θ. Is this estimator asymptotically unbiased?
- Find two positive integers such that their sum is 10, and minimize the sum of squares.Determine the uncertainties in x2 and y2 using the rule for propagating uncertainties when multiplying two numbers. x=80, y=60, ∆x= ∆y=5.Suppose that in a research it was discovered that those who majored in math, engineering, or computer science scored higher on tests measuring "problem-solving" ability at the end of 4 years of college than did those students who did not major in these fields. A. What is (are) the independent variable(s)?