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1. Let yˆ = E (y|x) be the conditional expectation of y given x. Prove that E{(y - yˆ)² } ≤ E{(y - π)² }, where π = π(x) is any other function of x. Show that E {x(y - yˆ)} = 0 and give an interpretation of this condition. Demonstrate that, if E (y|x) is a linear function of x, then we have E(y|x) = E(y) + β { x - E(x)} , where β = C (x, y)/ V (x).
A 100 ft length of steel chain weighing 15 lb/ft is hanging from the top of a tall building. How much work is done in pulling all of the chain to the top of the building?
john went to the store. he bouht a lamp for 56.56 that was on sale 20 percent then you can talk an additional 50
in a survey of 8000 woman 5431 say they change their nail polish once a week. construct a 99 confidence interval for
Use the approximate operation counts n2 /2 for back substitution and n3 /3 for elimination to estimate how long it will take to do a complete Gaussian elimination of this size. Round your answer to the nearest second.
Find the equation of the circle that has its center at the focus of the parabola X^2 - 4x + 6y - 20 = 0 and that is tangent to the parabola at its vertex. Also sketch both curves.
Estimate the expected grade & variance for the course
You are designing a rectangular poster to contain 256 in2 of printing with a 3-in. margin at the top and bottom and a 2-in. margin at each side. What overall dimensions will minimize the amount of paper used?
Assuming air resistance is negligible, the rocket is launched from a height of 2 feet, and the maximum height attained by the water rocket is 66 feet, determine the initial velocity of the rocket. That is, find the velocity of the rocket at the mo..
Present your final solutions as decimal approximations carried out to the third decimal place. Due to the nature of these solutions, no check is required.
Among those taking the Graduate Record Exam , 18 people are randomly selected. This group had a mean score of 550 and a population standard deviation of 140. What is the 95% confidence interval for the population mean for the GRE test. Identify th..
Strontium 90 is a radioactive material that decays according to the function A(t)=Ae^(-.0244t), where A is the initial amount present and A is the amount present at time t (years). What is the half-life of strontium 90? The answer is 28.4 years. H..
What is the shortest length of fence that the rancher can use? Note: The answer to this problem requires that you enter the correct units.
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