2. Prove or disprove that for any two events A, and A2,P[A, n Az] 21- PÍA4] – P[AG]

Answered: Image /qna-images/answer/2ec54a79-20a6-4352-810d-ded74bc8f857.jpg

Answered: Prove or disprove that for any two…

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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We are at a city named Freezo, close to the North Pole, where the days are either "warm" or "cold" (with temperature either above of below freezing). Assume that if we have a cold day today, then tomorrow will be also be cold with probability p (and warm with probability 1 – p), and if today is warm then tomorrow will be warm with probability q (and cold with probability 1 – q). Here p and q are some numbers in the interval (0, 1). Consider a matrix p 1- A = (8a) Prove that 1 = 1 is an eigenvalue of A (for any choice of p and q). (8b)| ] Set p = 3/4 and q = 1/2. Find the eigenvector of A corresponding to 1 = 1, such that x + y = 1. (8c) e It turns out that the numbers x and y that you found in (8b) represent the long-term probability that any given day will be cold and warm, respectively. We are planning a 30-day event "Snowtopia" in 2031 that requires at least 18 cold days during the event. Is Freezo a suitable place to host this event? Explain why.
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Prove or disprove that for any two events A, and A2, P[A, n A-] 21- PÍAG] – P[A£]