Give a combinatorial proof of (9^n) = (Sigma(k=0,n))(-1)^(k)(n choose k)(10)^(n-k)
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Give a combinatorial proof of (9^n) = (Sigma(k=0,n))(-1)^(k)(n choose k)(10)^(n-k)
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- What is the probability that given a block n of 30 bits, that you have an error sequence E(X)=P(X) where P(X) has 4 non-zero coefficients? Assume the probability of an individual bit error is .1 O 6.5x10^(-6) O 10^(-10) O 10^(-1) .3Let n > 3 and 2 (;) ')<(3) k n – k + + in two ways: (a) algebraic proof, and (b) combinatorial proof Hint for (b): show that the left side counts only some of the things counted by the right side.10 Σ13k2- 2k + 3(-1)*)
- Determine the coefficient of x^-2 in the full expansion of (x + 1/x)^(10)3. In 1917, L.L. Thurstone, a pioneer in quantitative learning theory proposed a model of the number of successful acts per unit time, A, that a person could accomplish after n, practice sessions. 55(n+1) n+8 Suppose that the function reflecting this information is given by_4(n)= a) Is A(n)increasing or decreasing over time? Does this make sense? b) What does A(n) approach as n increases? c) Sketch a graph of the function. d) How many practice sessions would it take for the person to be able to perform 20 successful acts? Answers: 3a) increasing b) 55 c) 3What is the coefficient of x^n for the generating function (1)/(1+x)^2?
