MATH 3670 Midterm: MATH 3670 GT sol3770 2 Spring10

• School: Georgia Tech
• Department: Mathematics
• Course: MATH 3670
• Professor: All

Document Summary

Compute: the marginal p. m. f. px1 (x1) and the conditional p. m. f. px2|x1 (x2|x1). px1 ( 1) = 0. 125 px1 (0) = 0. 75 px1 (1) = 0. 125 px2|x1 ( 1|0) = 3 px2|x1 ( 1|1) = 0 px2|x1 (0|1) = 1 px2|x1 ( 1| 1) = 0 px2|x1 (0| 1) = px2|x1 (1| 1) = 0. 6 px2|x1 (1|1) = 0: e(x1), v (x1), cov(x1, x2). E(x1) = 0. 125 ( 1) + 0. 75 (0) + 0. 125 (1) = 0. E(x1x2) = 0. 125 (0 1)+0. 125 (0 1)+0. 125 (1 0)+0. 125 ( 1 0)+0. 5 (0 0) = 0 since, by symmetry, e(x1) = e(x2) and v (x1) = v (x2), we have. Finally px1 (0)px2 (0) = 0. 752 6= 0. 5 = p(0, 0) so that they are not independent: the following data are the lifetimes xi, in months, of a sample of n = 20 bulbs. Assume that the lifetimes xi of the bulbs are inde-