Final Exam

1.Which of the following best defines a discrete random variable?

2.Let X be a random variable representing the outcome of a single roll of a fair six-sided die. What is the expectation value, E[X]?

3.Let X and Y be two random variables. The property E[aX + bY] = aE[X] + bE[Y] for any constants a and b is known as:

4.In decision theory, if you have to choose between two actions, Action A with an expected utility of 150 and Action B with an expected utility of 120, which action should you choose to maximize utility?

5.An insurance company calculates that there is a 1% chance of a policyholder filing a $10,000 claim and a 99% chance of filing no claim. To break even, what is the minimum premium the company should charge?

6.In actuarial science, the expected number of claims an insurance company will receive over a specific period is a critical calculation. True or false: This calculation directly influences the setting of insurance premiums.

7.A manager is deciding how much stock of a product to keep. Ordering too much leads to storage costs, while ordering too little leads to lost sales. This problem is a classic application of expectation value in which field?

8.In game theory, a player calculates the expected payoff of a strategy by:

9.An economist builds a model to predict the expected GDP growth for the next year based on current economic indicators. This is an application of expectation in:

10.In machine learning, a model's performance is often evaluated using a loss function. What does the 'expected loss' represent?

11.Which property of expectation allows us to calculate the expected sum of the outcomes of two dice rolls by simply summing their individual expected values, i.e., E[Roll1 + Roll2] = E[Roll1] + E[Roll2]?

12.You are playing a game where you win $5 if a coin flip is heads and lose$ 3 if it is tails. If the coin is fair (50% chance for heads or tails), what is the expected value of playing this game once?

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