Reference no: EM13985369
1. Let X1, X2, . . . , X8 be independent Exp(1)-distributed random variables with order statistic (X(1), X(2), . . . , X(8)). Find E(X(7) | X(5) = 10).
2. Let X1, X2, X3 be independent U (0, 1)-distributed random variables, and let X(1), X(2), X(3) be the order statistic. Prove the intuitively reasonable result that X(1) and X(3) are conditionally independent given X(2) and determine this (conditional) distribution. Remark. The problem thus is to determine the distribution of (X(1), X(3)) | X(2) = x.
3. The random variables X1, X2, and X3 are independent and Exp(1)- distributed. Compute the correlation coefficient ρX(1) ,X(3) .
4. Let X1 and X2 be independent, Exp(a)-distributed random variables.
a) Show that X(1) and X(2) - X(1) are independent, and determine their distributions.
b) Compute E(X(2) | X(1) = y) and E(X(1) | X(2) = x).
5. Let X1, X2, and X3 be independent, U (0, 1)-distributed random variables. Compute P (X(3) > 1/2 | X(1) =x).
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Two-dimensional normal distribution
: 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.
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Compute the direction the loop will want to rotate
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Determine the emf induced in the coil
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Timothy reverson an african american
: Timothy Reverson, an African American, has been employed with Cameron Lake Boat Rentals for 15 years. He is one of 17 employees. After an argument with his boss over a pay raise, Timothy is discharged. Timothy brings a lawsuit under Title VII afte..
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Compute the correlation coefficient
: The random variables X1, X2, and X3 are independent and Exp(1)- distributed. Compute the correlation coefficient ρX(1) ,X(3). Let X1 and X2 be independent, Exp(a)-distributed random variables.
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What direction does the induced current flow
: The magnetic field perpendicular to a circular wire loop 14.4 cm in diameter is changed from +0.35 T to -0.64 Tin 300 ins , where + means the field points away from an observer and - toward the observer. Calculate the induced emf. Express your answ..
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How much should be invested in each group of stocks
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The engineering department has uncovered
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Pick one of the pieces from each stick
: Remark. A concrete example runs as follows: Take 3 sticks of length 1, break each of them uniformly at random, and pick one of the pieces from each stick. Find the probability that the 3 chosen pieces can be constructed into a triangle.
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