chapter 1

Chapter 3: Discrete Random Variables and Probability Distributions69.a. h(x; 10,10,20) (the successes here are the top 10 pairs, and a sample of 10 pairs is drawnfrom among the 20)b. Let X = the number among the top 5 who play E-W. Then P(all of top 5 play the samedirection) = P(X = 5) + P(X = 0) = h(5;10,5,20) + h(5;10,5,20)c. N = 2n; M = n; n = nh(x;n,n,2n)E(X) =V(X) =nn 1n2 n=2⋅ ;⎛15⎞⎛15⎞⎜ ⎟ ⎜ ⎟⎝ 5 ⎠ 10= +⎝ ⎠= . 033⎛20⎞⎛20⎞⎜ ⎟ ⎜ ⎟⎝10⎠⎝10⎠⎛ 2n− n ⎞ n ⎞ ⎛ ⎞ ⎞ ⎛ ⎞ ⎛ ⎞⎜⎛ n n n⎜⎛ n n n 1⎜ ⎟ ⋅ n ⋅ ⋅ 1 − ⎟ = ⎜ ⎟ ⋅ ⋅ 1 − ⎟ = ⎜ ⎟ ⋅ ⋅ ⎜ ⎟⎝ 2n− 1 ⎠ 2n⎝ 2n⎠ ⎝ 2n−1⎠ 2 ⎝ 2n⎠ ⎝ 2n−1⎠2 ⎝ 2 ⎠70.a. h(x;10,15,50)M ⎞; ⎟N ⎠b. When N is large relative to n, h(x; n,M,N) = & b x n,,so h(x;10,150,500) =& b( x; 10,.3)c. Using the hypergeometric model, E(X) = 10 ⋅ = 3 and490V(X) = (10)(.3)(.7) = .982(2.1) = 2. 06499Using the binomial model, E(X) = (10)(.3) = 3, andV(X) = 10(.3)(.7) = 2.1⎛⎜⎝⎛150⎞⎜ ⎟⎝ 500 ⎠116