**Problem 1:**Find the value of $ c $ to make $ f(x) = \frac{cx}{2x-1} $, where $ x = 2, 3, 4 $, into a valid probability distribution.Enter answer as a reduced fraction.**Solution:**c = \[ \_\_ \] To make the function $ f(x) = \frac{cx}{2x-1} $ a valid probability distribution over the values $ x = 2, 3, 4 $, the sum of the probabilities must equal 1. Therefore, calculate the sum:\[ f(2) + f(3) + f(4) = \left(\frac{c \cdot 2}{2 \cdot 2 - 1}\right) + \left(\frac{c \cdot 3}{2 \cdot 3 - 1}\right) + \left(\frac{c \cdot 4}{2 \cdot 4 - 1}\right) = 1 \]Solve for $ c $, ensuring the result is a reduced fraction.

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Description: **Problem 1:**Find the value of \( c $ to make $ f(x) = \frac{cx}{2x-1} $, where $ x = 2, 3, 4 $, into a valid probability distribution.Enter answer as a reduced fraction.**Solution:**c = \[ \_\_ \] To make the function \( f(x) = \frac{cx}{2x-1

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1. Find the value of c to make f (x) = x = 2, 3, 4 into a valid probability distribution. Enter answer as a reduced fraction. C =

A First Course in Probability (10th Edition)

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Author:Sheldon Ross

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Chapter1: Combinatorial Analysis

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

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Question

**Problem 1:**

Find the value of $ c $ to make $ f(x) = \frac{cx}{2x-1} $, where $ x = 2, 3, 4 $, into a valid probability distribution.

Enter answer as a reduced fraction.

**Solution:**

c = \[ \_\_ \]

To make the function $ f(x) = \frac{cx}{2x-1} $ a valid probability distribution over the values $ x = 2, 3, 4 $, the sum of the probabilities must equal 1. Therefore, calculate the sum:

\[ f(2) + f(3) + f(4) = \left(\frac{c \cdot 2}{2 \cdot 2 - 1}\right) + \left(\frac{c \cdot 3}{2 \cdot 3 - 1}\right) + \left(\frac{c \cdot 4}{2 \cdot 4 - 1}\right) = 1 \]

Solve for $ c $, ensuring the result is a reduced fraction.

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