Recent content by changeofplans

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    Calculating Expected Value of a Random Variable: Solving for E[X]

    Homework Statement Suppose that X takes on one of the values 0, 1, and 2. If for some constant c, P{X = i} = cP{X = i - 1}, i = 1, 2. Find E [X] Homework Equations The Attempt at a Solution I'm not sure how to start this. A push in the right direction would be awesome. Thanks!
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    Ways to seat r out of n people around a table

    Okay, that makes sense. So now I have: \frac{P(n,r)}{r} What about multiplying r by 2, for the mirrored positions? \frac{P(n,r)}{2r} = \frac{n!}{\frac{(n-r)!}{2r}}
  3. C

    Ways to seat r out of n people around a table

    Homework Statement Find a formula for the number of ways to seat r of n people around a circular table, where seatings are considered the same if every person has the same two neighbors without regard to which side these neighbors are sitting on. Homework Equations None The Attempt...
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    Inclusion-exclusion positive integers

    Would it be the floor of \frac{pq}{p}? And then the number of multiples of q less than n would be the floor of \frac{pq}{q}. If that's the case, I think I see what I'm supposed to do; add up the primes in p, and add up the primes in q. Because they're not mutually exclusive, we then need to...
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    Inclusion-exclusion positive integers

    Homework Statement Suppose that p and q are prime numbers and that n = pq. Use the principle of inclusion-exclusion to find the number of positive integers not exceeding n that are relatively prime to n. Homework Equations Inclusion-Exclusion The Attempt at a Solution The...