# hw4 - Var(X = 10 Var(Y = 5 Cov(X Y = 5 Find the marginal...

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Home work 4 Due on Tuesday October 25, 2011 at the beginning of the class A. Solve the following problems in chapter 5: 7 th Edition: 10, 12, 28, 34, 54, 58, 78, 92, 106,136. 6 th Edition: 8, 10, 24, ??, 46, 50, 66,78, 90, 116. B. Solve the following problems in chapter 6: 7 th Edition: 1a, c, d, e, 4, 23b, c, 24, 39, 40, 42, 49 6 th Edition: 1a, c, d, e, 4, 19b, c, 20, 33, 34, 36, 43. Hint: In 1 d and e, solve only for U1 and U3. C . Assume the following joint probability distribution: P(x,y) y 2 5 8 1 0.1 0.1 0.1 x 3 0 0.2 0.2 5 0 0 0.3 Find the covariance and correlation coefficient using Excel. Turn in the Excel spreadsheet. D. Do this in Excel. Consider a bivariate normal distribution with values from your UIN: E(X) = last digit E(Y) = next to last digit.
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Unformatted text preview: Var(X) = 10 Var (Y) = 5 Cov (X, Y) = 5 Find the marginal distribution of y. (Form of distribution and parameters.) Find the conditional distribution of y given x = 3 Find the conditional distribution of x given y = -2. Use the formulas that are in question 5.129, 7 th edition [ 5.109, 6 th edition ] in your book. You do not need to prove the formulas. Find the value of the correlation coefficient. E . The probability density function if the failure time of a pump is uniform (i.e. it has a constant value, k ) between 0 and 100 months and zero elsewhere. a) Find k b) Find and plot the hazard function, h(t) . c) Find the expected life of the pump....
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