**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 $Var(X)$.

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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

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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 $Var(X)$.

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