Chapter 15: Q6P (page 749)

A card is drawn from a shuffled deck. Let $x = 10$ if it is an ace or a face card; $x = - 1$ if it is a $2$ ; and $x = 0$ otherwise.

Short Answer

Expert verified

The required values are mentioned below.

$\begin{matrix} μ = 3 \\ var (x) = \frac{284}{13} \\ σ = 4.67 \end{matrix}$

Step by step solution

Given Information

A card is drawn from a shuffled deck.

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 mean is given below.

$\begin{matrix} μ = \sum x_{i} P_{i} \\ μ = \frac{10 \times 16}{52} - \frac{1 \times 4}{52} \\ μ = 3 \end{matrix}$

The variance is given below.

$\begin{matrix} var (x) = \sum {(x_{i} - μ)}^{2} p (x_{i}) \\ var (x) = {(10 - 3)}^{2} \times \frac{16}{52} + {(- 1 - 3)}^{2} \times \frac{4}{52} + 3^{2} \times \frac{32}{52} \\ var (x) = \frac{284}{13} \end{matrix}$

The standard deviation is given below.

$\begin{matrix} σ = \sqrt{var (x)} \\ σ = \sqrt{\frac{284}{13}} \\ σ = 4.67 \end{matrix}$

Thegraph is shown below.

Hence, the required values are mentioned below.

$\begin{matrix} μ = 3 \\ var (x) = \frac{284}{13} \\ σ = 4.67 \end{matrix}$

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A card is drawn from a shuffled deck. Let $x = 10$ if it is an ace or a face card; $x = - 1$ if it is a $2$ ; and $x = 0$ otherwise.

Short Answer

Step by step solution

Given Information

Definition of the cumulative distribution function.

Find the values.

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A card is drawn from a shuffled deck. Let x=10if it is an ace or a face card; x=−1if it is a2 ; andx=0 otherwise.

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

Electromagnetism

Engineering Physics

Space Physics

Medical Physics

Electrostatics

Study anywhere. Anytime. Across all devices.

A card is drawn from a shuffled deck. Let $x = 10$ if it is an ace or a face card; $x = - 1$ if it is a $2$ ; and $x = 0$ otherwise.