The probability density function of a discrete random variable X is given by the following table: Px(X = 0) = .073 Px(X = 1) = .117 Px(X = 2) = .258 Px(X = 3) = .322 %3D Px(X = 4) .230 i) Compute E(X). ii) Compute Var(X).
The probability density function of a discrete random variable X is given by the following table: Px(X = 0) = .073 Px(X = 1) = .117 Px(X = 2) = .258 Px(X = 3) = .322 %3D Px(X = 4) .230 i) Compute E(X). ii) Compute Var(X).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 19E
Related questions
Question
![**Probability Density Function and Statistical Calculation**
The probability density function of a discrete random variable \(X\) is given by the following table:
\[P_X(X = 0) = 0.073\]
\[P_X(X = 1) = 0.117\]
\[P_X(X = 2) = 0.258\]
\[P_X(X = 3) = 0.322\]
\[P_X(X = 4) = 0.230\]
To solve the given problems:
i) **Compute \(E(X)\):**
The expected value \(E(X)\) of a discrete random variable \(X\) can be calculated using the formula:
\[E(X) = \sum_{i} x_i \cdot P(X = x_i)\]
ii) **Compute \(Var(X)\):**
The variance \(Var(X)\) is given by:
\[Var(X) = E(X^2) - [E(X)]^2\]
Where \(E(X^2)\) is the expected value of the square of \(X\) and can be calculated as:
\[E(X^2) = \sum_{i} x_i^2 \cdot P(X = x_i)\]
These calculations involve summing over all the possible values of \(X\) weighted by their respective probabilities. Substituting the given values from the table will provide the numerical results for \(E(X)\) and \(Var(X)\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F45fdd75f-924d-4ac4-9d15-03fc1f26bc02%2Fa20673dc-387b-409a-9d50-b00135fa6d68%2Fzns79r_processed.png&w=3840&q=75)
Transcribed Image Text:**Probability Density Function and Statistical Calculation**
The probability density function of a discrete random variable \(X\) is given by the following table:
\[P_X(X = 0) = 0.073\]
\[P_X(X = 1) = 0.117\]
\[P_X(X = 2) = 0.258\]
\[P_X(X = 3) = 0.322\]
\[P_X(X = 4) = 0.230\]
To solve the given problems:
i) **Compute \(E(X)\):**
The expected value \(E(X)\) of a discrete random variable \(X\) can be calculated using the formula:
\[E(X) = \sum_{i} x_i \cdot P(X = x_i)\]
ii) **Compute \(Var(X)\):**
The variance \(Var(X)\) is given by:
\[Var(X) = E(X^2) - [E(X)]^2\]
Where \(E(X^2)\) is the expected value of the square of \(X\) and can be calculated as:
\[E(X^2) = \sum_{i} x_i^2 \cdot P(X = x_i)\]
These calculations involve summing over all the possible values of \(X\) weighted by their respective probabilities. Substituting the given values from the table will provide the numerical results for \(E(X)\) and \(Var(X)\).
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning