ichbindeutsch2005
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1. A game is devised in which a single die is thrown. A gambler agrees to pay out in dollars the amount shown on the die if the number is odd, and to collect the amount shown on the die if the number is even. What is his mathematical expectation?
2. Prove that the probability of obtaining at least r successes in n trials of a Bernoulli trial experiment, where the probability of success on a single trial is p, is given by Pr[at least r successes in n trials] = (n/r)p^r(1-p)^(n-r) + (n/(r+1))p^(r+1)*(1-p)^(n-r-1)+...+(n/n)p^n(1-p)^0
3. Combine Hudde's and Leiniz' methods to compute the derivative of y = x^n at an arbitrary point [x,y]
2. Prove that the probability of obtaining at least r successes in n trials of a Bernoulli trial experiment, where the probability of success on a single trial is p, is given by Pr[at least r successes in n trials] = (n/r)p^r(1-p)^(n-r) + (n/(r+1))p^(r+1)*(1-p)^(n-r-1)+...+(n/n)p^n(1-p)^0
3. Combine Hudde's and Leiniz' methods to compute the derivative of y = x^n at an arbitrary point [x,y]