How would I find the expected difference of this function? ### Piecewise Function DescriptionIn mathematics, a piecewise function is defined by different expressions for different intervals of the domain. Here, we have a two-variable function $ f(x,y) $ defined as follows:\[ f(x,y) = \begin{cases} \frac{3} {380000} (x^2 + y^2) & \text{if } 20 \leq x \leq 30 \text{ and } 20 \leq y \leq 30 \\0 & \text{otherwise}\end{cases} \]Let's break this down:- For $ x $ and $ y $ values within the inclusive range of 20 to 30, the function $ f(x,y) $ is given by: \[ f(x,y) = \frac{3} {380000} (x^2 + y^2) \] - For $ x $ and $ y $ values outside the aforementioned range, the function $ f(x,y) $ takes on a value of 0.**Explanation:**1. **Case 1: $ 20 \leq x \leq 30 $ and $ 20 \leq y \leq 30 $** - Within this range, the function combines the squares of the variables $ x $ and $ y $ and multiplies the result by $\frac{3}{380000}$.2. **Case 2: Otherwise** - If $ x $ and $ y $ values do not fall within the defined range (either $ x $ or $ y $ or both fall outside 20 to 30), the function equals zero.This type of function is useful in modeling real-world phenomena where different rules apply to different ranges of data.

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Description: How would I find the expected difference of this function? ### Piecewise Function DescriptionIn mathematics, a piecewise function is defined by different expressions for different intervals of the domain. Here, we have a two-variable function \( f(x,

From the given information, the joint density function for X and Y is, Consider,

Answered: 3 (x² + y²) 20 < x < 30, 20

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3 (x² + y²) 20 < x < 30, 20

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Question

How would I find the expected difference of this function?

### Piecewise Function Description

In mathematics, a piecewise function is defined by different expressions for different intervals of the domain. Here, we have a two-variable function $ f(x,y) $ defined as follows:

\[ f(x,y) = \begin{cases}
\frac{3} {380000} (x^2 + y^2) & \text{if } 20 \leq x \leq 30 \text{ and } 20 \leq y \leq 30 \\
0 & \text{otherwise}
\end{cases} \]

Let's break this down:

- For $ x $ and $ y $ values within the inclusive range of 20 to 30, the function $ f(x,y) $ is given by:
\[
f(x,y) = \frac{3} {380000} (x^2 + y^2)
\]

- For $ x $ and $ y $ values outside the aforementioned range, the function $ f(x,y) $ takes on a value of 0.

**Explanation:**

1. **Case 1: $ 20 \leq x \leq 30 $ and $ 20 \leq y \leq 30 $**
- Within this range, the function combines the squares of the variables $ x $ and $ y $ and multiplies the result by $\frac{3}{380000}$.

2. **Case 2: Otherwise**
- If $ x $ and $ y $ values do not fall within the defined range (either $ x $ or $ y $ or both fall outside 20 to 30), the function equals zero.

This type of function is useful in modeling real-world phenomena where different rules apply to different ranges of data.

Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.

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