Chapter 15: Q4P (page 749)

Suppose that Martian dice are 4-sided (tetrahedra) with points labeled $1 - 4$ . When a pair of these dice is tossed, let x be the product of the two numbers at the tops of the dice if the product is odd; otherwise $x = 0$ .

Short Answer

Expert verified

The required values are mentioned below.

$\begin{matrix} μ = 1 \\ var (x) = \frac{21}{4} \\ σ = \frac{\sqrt{21}}{2} \end{matrix}$

Step by step solution

Given Information

Martian dice is tossed

Definition of the cumulative distribution function

The likelihood that a comparable continuous random variable has a value less than or equal to the function's argument is the value of the function.

Find the values

The random variables are given below.

$\begin{matrix} x_{1} = 1 \\ p (x_{1}) = 1 / 16 \\ x_{2} = 0 \\ p (x_{2}) = 2 / 16 \end{matrix}$

Solve further.

$\begin{matrix} x_{3} = 3 \\ p (x_{3}) = 2 / 16 \\ x_{4} = 0 \\ p (x_{4}) = 3 / 16 \end{matrix}$

Solve further.

$\begin{matrix} x_{6} = 0 \\ p (x_{6}) = 2 / 16 \\ x_{8} = 0 \\ p (x_{8}) = 2 / 16 \end{matrix}$

Solve further.

$\begin{matrix} x_{9} = 9 \\ p (x_{9}) = 1 / 16 \\ x_{12} = 0 \\ p (x_{12}) = 2 / 16 \end{matrix}$

Solve further.

$\begin{matrix} x_{16} = 0 \\ p (x_{16}) = 1 / 16 \end{matrix}$

The mean is given below.

$\begin{matrix} μ = \sum x_{i} p (x_{i}) \\ μ = \frac{1}{16} + \frac{6}{19} + \frac{9}{16} \\ μ = 1 \end{matrix}$

The variance is given below.

$\begin{matrix} var (x) = \sum {(x_{i} - μ)}^{2} p (x_{i}) \\ var (x) = \frac{2}{16} + \frac{3}{16} + \frac{2}{16} + \frac{2}{16} + \frac{1}{16} + \frac{4 \times 2}{16} + \frac{64}{16} \\ var (x) = \frac{21}{4} \end{matrix}$

The standard deviation is given below.

$\begin{matrix} σ = \sqrt{var (x)} \\ σ = \sqrt{\frac{21}{4}} \\ σ = \frac{\sqrt{21}}{2} \end{matrix}$

The graph is shown below.

Hence, the required values are mentioned below.

$\begin{matrix} μ = 1 \\ var (x) = \frac{21}{4} \\ σ = \frac{\sqrt{21}}{2} \end{matrix}$

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Suppose that Martian dice are 4-sided (tetrahedra) with points labeled $1 - 4$ . When a pair of these dice is tossed, let x be the product of the two numbers at the tops of the dice if the product is odd; otherwise $x = 0$ .

Short Answer

Step by step solution

Given Information

Definition of the cumulative distribution function

Find the values

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Most popular questions from this chapter

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Suppose that Martian dice are 4-sided (tetrahedra) with points labeled 1−4. When a pair of these dice is tossed, let x be the product of the two numbers at the tops of the dice if the product is odd; otherwisex=0.

Short Answer

Step by step solution

Given Information

Definition of the cumulative distribution function

Find the values

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Magnetism

Rotational Dynamics

Fields in Physics

Circular Motion and Gravitation

Radiation

Energy Physics

Study anywhere. Anytime. Across all devices.

Suppose that Martian dice are 4-sided (tetrahedra) with points labeled $1 - 4$ . When a pair of these dice is tossed, let x be the product of the two numbers at the tops of the dice if the product is odd; otherwise $x = 0$ .