Please help **Transcription and Explanation for Educational Website**---### Problem StatementA random variable has density function \( f(x) = 1.6 - 1.2x \), for \( 0 \leq x \leq 1 \).#### a) Calculate the variance of \( X \).\[ \text{Var}(X) = 0.073 \; \text{\red{✗}} \]The calculation shown for the variance of \( X \) is marked incorrect.#### b) Calculate the variance of \( g(X) = 3X + 1 \).\[ \text{Var}(g(X)) = 0.657 \; \text{\red{✗}} \]The calculation for the variance of \( g(X) \) is also marked incorrect.---### ExplanationThis image presents a problem related to calculating variances for a random variable characterized by a given probability density function (PDF). The function is defined on the interval \( [0, 1] \).**Density Function:**- \( f(x) = 1.6 - 1.2x \) is the PDF over the specified range.**Tasks:**1. **Variance of \( X \):** - Calculate the variance using the given density function.2. **Variance of \( g(X) = 3X + 1 \):** - Apply transformation properties for variance: - If \( g(X) = aX + b \), then \( \text{Var}(g(X)) = a^2 \text{Var}(X) \).Both answers provided for \( \text{Var}(X) \) and \( \text{Var}(g(X)) \) were incorrect, which suggests a reevaluation of the integration and transformation steps is needed.**Note:** Calculating the correct variance involves integrating the square of deviation from the mean weighted by the density function.

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A random variable has density function f(x) = 1.6 - 1.2x, for 0≤x≤1. a) Calculate the variance of X. Var (X) = = 0.073 X

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...