### Probability and Statistics Exercise#### Task Descriptions:**(b)** Compute $ P(x < 25) $.- **Given Answer:** 0.5 ✔️**(c)** Compute $ P(23 \leq x \leq 25) $.- **Given Answer:** 0.2 ✔️**(d)** Compute $ E(x) $.- **Answer Box:** [ ]**(e)** Compute $ \text{Var}(x) $. (Round your answer to two decimal places.)- **Answer Box:** [ ]### Notes:- Part (b) and (c) have provided solutions with check marks indicating correctness.- Parts (d) and (e) require computing the expected value and variance, respectively. Fill in the answer boxes with the appropriate numerical values. **Uniform Distribution Example: Probability Density Function****Given:**The random variable $ x $ is uniformly distributed between 20 and 30.**Task:**(a) Show the graph of the probability density function.**Graph Description:**- **Axes:** - The horizontal axis is labeled $ x $. - Tick marks on the horizontal axis are at 10, 20, 30, 40, and 50. - The vertical axis is labeled $ f(x) $. - Tick marks on the vertical axis are at 0.05, 0.1, 0.15, and 0.2.- **Shaded Area:** - Represents the probability density function for $ x $ from 20 to 30. - A vertical line segment of 0.05 units at $ x = 20 $. - A vertical line segment of 0.05 units at $ x = 30 $. - A horizontal line segment of 10 units connects the tops of these vertical lines, starting at $ x = 20 $ right above the tick mark labeled 0.05 on the vertical axis and extending to $ x = 30 $.This graph visually represents the uniform distribution, showing constant probability density between $ x = 20 $ and $ x = 30 $, as indicated by the shaded rectangle.

Therefore, Expected value of x is given by

Answered: The random variable x is known to be…

The random variable x is known to be uniformly distributed between 20 and 30. (a) Show the graph of the probability density function. fin

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

### Probability and Statistics Exercise

#### Task Descriptions:

**(b)** Compute $ P(x < 25) $.

- **Given Answer:** 0.5 ✔️

**(c)** Compute $ P(23 \leq x \leq 25) $.

- **Given Answer:** 0.2 ✔️

**(d)** Compute $ E(x) $.

- **Answer Box:** [ ]

**(e)** Compute $ \text{Var}(x) $. (Round your answer to two decimal places.)

- **Answer Box:** [ ]

### Notes:
- Part (b) and (c) have provided solutions with check marks indicating correctness.
- Parts (d) and (e) require computing the expected value and variance, respectively. Fill in the answer boxes with the appropriate numerical values.

**Uniform Distribution Example: Probability Density Function**

**Given:**
The random variable $ x $ is uniformly distributed between 20 and 30.

**Task:**
(a) Show the graph of the probability density function.

**Graph Description:**

- **Axes:**
- The horizontal axis is labeled $ x $.
- Tick marks on the horizontal axis are at 10, 20, 30, 40, and 50.
- The vertical axis is labeled $ f(x) $.
- Tick marks on the vertical axis are at 0.05, 0.1, 0.15, and 0.2.

- **Shaded Area:**
- Represents the probability density function for $ x $ from 20 to 30.
- A vertical line segment of 0.05 units at $ x = 20 $.
- A vertical line segment of 0.05 units at $ x = 30 $.
- A horizontal line segment of 10 units connects the tops of these vertical lines, starting at $ x = 20 $ right above the tick mark labeled 0.05 on the vertical axis and extending to $ x = 30 $.

This graph visually represents the uniform distribution, showing constant probability density between $ x = 20 $ and $ x = 30 $, as indicated by the shaded rectangle.

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