Homework 3 Answers

BSTA 550

Non-textbook problems

• #1 (a) \(X\sim binomial \big(\sum_{i=1}^m n_i, p\big)\)      (b) \(E(X) = p\sum_{i=1}^m n_i\)      (c) \(Var(X) = p(1-p)\sum_{i=1}^m n_i\)

Textbook problems

There are answers at the back of the book!! Selected answers (or hints) not provided at the end the book:

• Chapter 7

  • # 2: \(X\in(0,\infty)\), continuous; \(Y\in\{0,1,2,\ldots\}\), discrete

  • # 10: \(X_j\in[0,\infty),j=1,\ldots,100\); \(Y\in[0,\infty)\); both continuous

  • # 16: \(Y\) could be 0

  • # 18: Yes, a r.v. can be both. Give an example!

• Chapter 8

  • # 2: (a) \(p(x)=\binom{7}{x}(.5)^7\) for \(x=0,1,2,\ldots,7\)

  • # 9: (a) \(c = \frac{1}{8}\)

  • # 10:

    \(x\)	2	4	6	8
    \(p(x)\)	3/10	1/2	3/20	1/20

• Chapter 15

  • # 18  (a) Bin(21,0.65)     (b) 4.78     

• Chapter 16

  • # 8  (a) 14.28      (b) code below     (c) \(1.03\times 10^{-6}\)    (d) 10 questions: 91.43 minutes    

  1-pgeom(q = 18, prob = 0.07)

  [1] 0.2518698

  ## OR
  pgeom(q = 18, prob = 0.07, lower.tail = F)

  [1] 0.2518698

• Chapter 17

  • # 6   (a) 400, 87.18     (b) No     

  • # 12   (c) 0.8000

• Chapter 18

  • # 20 (a) (b) 0.6514 (c) 0.0598

  • # 24  (c) 0.8571

  • # 26  162,754.8

• Chapter 19

  • # 6:  (c) 15.625     (d) 0.0486     (f) 0.0488

  • # 18:   100

• Chapter 20

  • # 2:  (a) 0.0001     (b) Discrete since \(X\) has a finite number of possible values. Uniform since each outcome is equally likely.     (c) \(X\) = randomly selected 4-digit ID#; \(X=0000,0001,\ldots,9999\)     (d) 5000.5     (e) 8,333,333.25