​(b) Compute the mean and standard deviation of the random variable using

mu Subscript Upper XμXequals=Summation from nothing to nothing left bracket x times Upper P left parenthesis x right parenthesis right bracket∑[x•P(x)]

and

sigma Subscript Upper XσXequals=StartRoot Summation from nothing to nothing left bracket x squared times Upper P left parenthesis x right parenthesis right bracket minus mu Subscript Upper X Superscript 2 EndRoot∑x2•P(x)−μ2X.

mu Subscript Upper XμXequals=enter your response here

​(Round to two decimal places as​ needed.)

To calculate the **mean** \(\mu_X\) and **standard deviation** \(\sigma_X\) of a discrete random variable, we use the following formulas:

### 1. Mean (\(\mu_X\)):
\[
\mu_X = \sum [x \cdot P(x)]
\]
This means we take each value \(x\), multiply it by its corresponding probability \(P(x)\), and then sum these products.

### 2. Standard Deviation (\(\sigma_X\)):
\[
\sigma_X = \sqrt{ \sum [x^2 \cdot P(x)] - \mu_X^2 }
\]
This requires first calculating \(\sum [x^2 \cdot P(x)]\) and then subtracting the square of the mean, \(\mu_X^2\), from it. Finally, take the square root to find \(\sigma_X\).

#### Steps to compute:
1. **List the values of \(x\)** and their corresponding probabilities \(P(x)\).
2. **Compute \(\sum [x \cdot P(x)]\)** to find the mean \(\mu_X\).
3. **Compute \(\sum [x^2 \cdot P(x)]\)**.
4. Plug these into the formula for \(\sigma_X\) and compute the standard deviation.

Please provide the values of \(x\) and \(P(x)\) so I can help you compute the mean and standard deviation.

Compute the mean and standard deviation of the random variable using μX = ∑[x•P(x)] and σX = √[∑[x²•P(x)] - μX²].

Learn how to calculate the mean (μX) and standard deviation (σX) of a discrete random variable using probabilities. This solution provides step-by-step formulas and methods suitable for high school students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation