Question

1. the following table represents the number of points a football team can score on offense per possession with the probability of each. find the expected value of points scored per possession.
2. the following table represents the number of points a basketball team can score per possession with the probability of each. find the expected value of points scored per possession.
3. the following table represents the number of points a soccer team can score per game played with the probability of each. find the expected value of points scored per game.
4. the following table represents the possible money earned or lost on a single parlay bet with the probability of each. find the expected money earned per parlay bet.

Explanation:

Step1: Recall the formula for expected value

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

Step2: Calculate the expected value for problem 6

For problem 6:

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$$

Step3: Calculate the expected value for problem 7

For problem 7:

$$
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$$

Step4: Calculate the expected value for problem 8

For problem 8:

$$
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$$

Step5: Calculate the expected value for problem 9

For problem 9:

$$
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$$

Answer:

Problem 6: \(3.34\)
Problem 7: \(1.18\)
Problem 8: \(1.85\)
Problem 9: \(-\frac{5}{12}\approx - 0.42\)