Homework 5 Answers

BSTA 550

Non-textbook problems

• #1:

  • 1. \(X \sim \text{Binom}\bigg( \sum_{i=1}^m n_i, p \bigg)\)
  • 2. \(E(x) = p \cdot \sum_{i=1}^m n_i\)
  • 3. \(\text{Var}(X) = p \cdot (1-p) \cdot \sum_{i=1}^m n_i\)

• #2: 450

• #3: Hint: use the definition of variance

• #4: (a) \(E(\overline{X}) = \mu\)    (b) \(\text{Var}(\overline{X}) = \dfrac{\sigma^2}{n}\)

Textbook problems

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

• Chapter 10

  • # 6:  750.5

  • # 8:  0.9

  • # 10:   201

  • # 14:   (a) 1.875     (b) 3.125     

• Chapter 11

  • # 2:  1.6

  • # 18:  a) 48.5     (b) 96     

  • # 20:  \(\approx\) 23.077

• Chapter 12

  • # 2:  64.8

  • # 12:  1,096,357

• Chapter 13

  • # 4:  (a) 260/9     (b) 2.833     (c) \(2.679\times 10^{-5}\)     (d) Same idea as (c) Replace 10’s with 100.     

  • # 6:  (a) \(p_X(x)=\binom{4}{x}.3^x .7^{4-x}\), for \(x=0,1,\ldots,4\)     (d) 0.3483     (e) 0.9163     (f) 0.0233     (g) 1

  • # 8:  (a) T     (b) F     (c) F     (d) F     (e) T     (f) T    (g) T

  • # 10:  (a) T     (b) T    (c) F     (d) T    (e) T     (f) F    (g) T     (h) T (nonnegative instead of positive)     (i) F