Homework 6 Answers

BSTA 550

Non-textbook problems

• #1:

Textbook problems

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

• Calculus Review

  • (a)  \(c(\frac{y^{2}}{2}+y^{2})\)

  • (b)  \(\frac{8}{9}xy^{2}+\frac{5}{9}y^{4}\)

  • (c)  \(\frac{8}{9}x^{2}y+\frac{20}{9}xy^{3}\)

  • (d)  \(-2e^{-2y}+2e^{-y}\)

  • (e)  \(xe^{-x}\)

  • (f)  \(-\frac{2}{3}(e^{-7x}-e^{-4x})\)

  • (g)  \(\frac{9}{2}\)

  • (h)  \(\frac{9}{2}\)

  • (i)  \(\frac{9}{2}\)

  • (j)  \(\frac{9}{2}\)

• Chapter 24

  • # 2: (a) Discrete     (b) Discrete     (c) Continuous

  • # 19:

    • 1. \[F_X(x) = \left\{ \begin{array}{ll} 0 & \quad x \leq 16 \\ \frac{1}{64}x^2 - \frac{1}{2}x + 4 & \quad 16 < x\leq 24 \\ 1 & \quad x > 24 \\ \end{array} \right.\]
    • 2. \(a=20\)

  • # 20:

    • 1. \(k=660\)
    • 2. \[F_X(x) = \left\{ \begin{array}{ll} 0 & \quad x < 0 \\ 55x^{12} - 120x^{11} + 55x^{10} & \quad 0 \leq x\leq 1 \\ 1 & \quad x > 24 \\ \end{array} \right.\]

  • # 22: \[f_X(x) = \left\{ \begin{array}{ll} 0 & \quad x <0 \\ \frac{7x}{4} & \quad 0\leq x\leq 1 \\ 0 & \quad 1< x< 7 \\ \frac{1}{8} & \quad 7\leq x\leq 8 \\ 0 & \quad x>8 \\ \end{array} \right.\]