Question

the owner of a local movie theater keeps track of the number of tickets sold in each purchase and makes a probability distribution based on these records. let x represent the number of tickets bought in one purchase. the distribution for x is given in the table. what is the expected value of the distribution? 2 2.1 2.5 3

Explanation:

Step1: Recall the formula for expected value

The formula for the expected value \(E(X)\) of a discrete random variable is \(E(X)=\sum_{i}x_ip_i\), where \(x_i\) are the values of the random variable and \(p_i\) are their corresponding probabilities.

Step2: Calculate each term \(x_ip_i\)

• For \(x = 1\) and \(p=0.29\): \(1\times0.29 = 0.29\)
• For \(x = 2\) and \(p = 0.44\): \(2\times0.44=0.88\)
• For \(x = 3\) and \(p = 0.19\): \(3\times0.19 = 0.57\)
• For \(x = 4\) and \(p = 0.06\): \(4\times0.06=0.24\)
• For \(x = 5\) and \(p = 0.02\): \(5\times0.02 = 0.1\)

Step3: Sum up the terms

\(E(X)=0.29 + 0.88+0.57+0.24 + 0.1\)

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Answer:

2.1