**Title: Calculating the Expected Value of a Random Variable****Objective:** Learn how to find the expected value \( E(X) \) of a random variable \( X \) given its probability distribution.**Problem Statement:**Find the expected value \( E(X) \) of a random variable \( X \) having the following probability distribution. (Enter an exact number as an integer, fraction, or decimal.)**Incorrect Value Entered:** \( E(X) = 4.75 \)**Probability Distribution Table:**| \( x \) | -3 | -1 | 1 | 3 | 5 | 7 ||-----------|----|----|---|---|---|---|| \( P(X=x) \) | \( \frac{1}{8} \) | \( \frac{1}{4} \) | \( \frac{3}{16} \) | \( \frac{1}{4} \) | \( \frac{1}{16} \) | \( \frac{1}{8} \) |**Instructions:**1. Multiply each value of \( x \) by its corresponding probability \( P(X=x) \).2. Sum all these products to get the expected value \( E(X) \).**Notes:**- Ensure all fractions are simplified and all arithmetic is accurate to ensure the correct expected value calculation.- Compare your result with the initially entered incorrect value of 4.75 to verify accuracy.

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A First Course in Probability (10th Edition)

10th Edition

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Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

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

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A certain brand of cars captured 21.7% of the market. If 3 cars are selected at random, the probability distribution is given below. Find E(x). 1 2 3 P(x) 0.2 0.4 0.1 0,3 What is the expected value? E(x) = (Type an integer or a decimal.)
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Find the expected value E(X) of a random variable X having the following probability distribution. (Enter an exact number as an integer, fraction, or decimal.) E(X) = 4.75 -3 -1 1 5 1 3 1 P(X = x) 8 4 16 4 16 8