Q2 Solutions

# Q2 Solutions - Question 3 Explain why C k,n = P k,n/k For...

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Steven Weber Dept. of ECE Drexel University ENGR 361: Statistical Analysis of Engineering Systems (Fall, 2007) Quiz 2 Solutions (Wednesday, October 3) Question 1. Prove P ( A ) 1 for any event A ∈ E using the three axioms of probability. First, note that A, A are disjoint events, hence P ( A A ) = P ( A ) + P ( A ). Also, note that A A = S , and thus P ( A ) + P ( A ) = 1. Next, note that P ( A ) 0, which means 1 - P ( A ) 0, or P ( A ) 1. Question 2. Define a permutation and a combination. A permutation is an ordered subset, a combination is an unordered subset.
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Unformatted text preview: Question 3. Explain why C k,n = P k,n /k ! . For each combination of k elements there are k ! ways of ordering those elements, i.e., there are k ! distinct permutations for each combination. Hence, the number of combinations is obtained by dividing the number of permutations by k !. www.ece.drexel.edu/faculty/sweber 1 October 3, 2007...
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