Write a proof of the Law of Total Probability, which says that for a partition A1, A2,..., An of a sample space S (that is, the A, are all disjoint and their union is S), with P(A) > 0 for all i, we have 72 P(B) = P(B|A;)P(A;). i=1 Hint: I gave an illustration of the LOTP in class, but a picture is not a proof. Write your proof in complete sentences and mathematical statements (i.e. equations), clearly and logically explaining why the formula is true. Tip for those new to proofs: Be thorough! If you claim something, you need to back it up, so that the grader and I can't ask "where did this come from?" Chances are, we know where it came from because we've seen it before, but we want to know that YOU know where it came from! If you apply a formula, theorem, definition, etc., tell us which one.
Write a proof of the Law of Total Probability, which says that for a partition A1, A2,..., An of a sample space S (that is, the A, are all disjoint and their union is S), with P(A) > 0 for all i, we have 72 P(B) = P(B|A;)P(A;). i=1 Hint: I gave an illustration of the LOTP in class, but a picture is not a proof. Write your proof in complete sentences and mathematical statements (i.e. equations), clearly and logically explaining why the formula is true. Tip for those new to proofs: Be thorough! If you claim something, you need to back it up, so that the grader and I can't ask "where did this come from?" Chances are, we know where it came from because we've seen it before, but we want to know that YOU know where it came from! If you apply a formula, theorem, definition, etc., tell us which one.
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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Transcribed Image Text:Write a proof of the Law of Total Probability, which says that for a partition
A1, A2,..., An of a sample space S (that is, the A, are all disjoint and their union is S), with
P(A) > 0 for all i, we have
72
P(B) = P(B|A;)P(A;).
i=1
Hint: I gave an illustration of the LOTP in class, but a picture is not a proof. Write
your proof in complete sentences and mathematical statements (i.e. equations), clearly and
logically explaining why the formula is true.
Tip for those new to proofs: Be thorough! If you claim something, you need to back it
up, so that the grader and I can't ask "where did this come from?" Chances are, we know
where it came from because we've seen it before, but we want to know that YOU know
where it came from! If you apply a formula, theorem, definition, etc., tell us which one.
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