Consider the probability space (Ω,A , P) where Ω = R and A is the Borel σ-algebra on R. Suppose that for any n = 1, 2, . . . , we have P((−∞, 2−n]) = 1/2 and P((−∞, −2−n]) = 1/3 − 1/(4^n) . Given the above, compute the following probability values, if possible, showing complete justifi- cation for every step. If it is impossible to compute a value precisely, provide the tightest possible bounds on it. P((−∞, 0]) P({0}) P((−∞, −1]) P((1/4, π/7]) limn→∞ P((0, n])

Consider the probability space (Ω,A , P) where Ω = R and A is the Borel σ-algebra on R. Suppose that for any n = 1, 2, . . . , we have P((−∞, 2−n]) = 1/2 and P((−∞, −2−n]) = 1/3 − 1/(4^n) . Given the above, compute the following probability values, if possible, showing complete justifi- cation for every step. If it is impossible to compute a value precisely, provide the tightest possible bounds on it. P((−∞, 0]) P({0}) P((−∞, −1]) P((1/4, π/7]) limn→∞ P((0, n])

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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