sample_midterm_1_questions

... 1. Consider the following experiment. A fair coin is tossed, if the result is Heads, a sixsided die is rolled, otherwise a four-sided die is rolled. Both dice are unbiased. Let X be the number that shows up on the die.. a. Find the value of E[X] and Var[X]. b. Use the uniform random numbers in the t ...

... 1. Consider the following experiment. A fair coin is tossed, if the result is Heads, a sixsided die is rolled, otherwise a four-sided die is rolled. Both dice are unbiased. Let X be the number that shows up on the die.. a. Find the value of E[X] and Var[X]. b. Use the uniform random numbers in the t ...

Practice Problems for Exam 3

... If the customer dies this year, the company pays out $10000. Suppose the probability that any individual customer dies this year is 1%, and that all customers live and die independently. Let Q be the company’s proﬁt. Find the expected value and standard deviation of Q. (13) A random number generator ...

... If the customer dies this year, the company pays out $10000. Suppose the probability that any individual customer dies this year is 1%, and that all customers live and die independently. Let Q be the company’s proﬁt. Find the expected value and standard deviation of Q. (13) A random number generator ...

Random Variables - University of Arizona

... • The probability distribution can be written as a table, or as a histogram (called a probability histogram). • In order to be a legitimate probability distribution, the probabilities must fall between 0 and 1 and sum to 1. ...

... • The probability distribution can be written as a table, or as a histogram (called a probability histogram). • In order to be a legitimate probability distribution, the probabilities must fall between 0 and 1 and sum to 1. ...

Standard error of estimate & Confidence interval

... Standard error of an estimator Before knowing the value: “Standard deviation of the estimates in repeated sampling IF the true value of the parameter was ...

... Standard error of an estimator Before knowing the value: “Standard deviation of the estimates in repeated sampling IF the true value of the parameter was ...

7.2 Day 1: Mean & Variance of Random Variables

... μx = 1(1/9) + 2(1/9) + 3(1/9) + 4(1/9) + 5(1/9) + 6(1/9) + ...

... μx = 1(1/9) + 2(1/9) + 3(1/9) + 4(1/9) + 5(1/9) + 6(1/9) + ...

Name - Humble ISD

... 11. Insurance companies compute expected values so that they can set their rates at profitable but competitive levels. A 64 year-old man obtains a $10,000 one-year life insurance policy at a cost of $600 per month. Based on past mortality experience, the insurance company estimates that there is a 0 ...

... 11. Insurance companies compute expected values so that they can set their rates at profitable but competitive levels. A 64 year-old man obtains a $10,000 one-year life insurance policy at a cost of $600 per month. Based on past mortality experience, the insurance company estimates that there is a 0 ...

Quick Review: More Theorems for Conditional Expectation

... Detection and Diagnosis”, the risk of a false positive result in a mammogram is about 1 in 10. ...

... Detection and Diagnosis”, the risk of a false positive result in a mammogram is about 1 in 10. ...

Mean of a discrete random variable

... multiplying each outcome by its probability and then summing all possible outcomes. It is an average of the possible outcomes, but not the ordinary average that you are use to where everything is equal. The expected value represents the “long-run average” if we repeat the actual event many times. Ex ...

... multiplying each outcome by its probability and then summing all possible outcomes. It is an average of the possible outcomes, but not the ordinary average that you are use to where everything is equal. The expected value represents the “long-run average” if we repeat the actual event many times. Ex ...

In probability theory, the law of large numbers (LLN) is a theorem that describes the result of performing the same experiment a large number of times. According to the law, the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed.The LLN is important because it ""guarantees"" stable long-term results for the averages of some random events. For example, while a casino may lose money in a single spin of the roulette wheel, its earnings will tend towards a predictable percentage over a large number of spins. Any winning streak by a player will eventually be overcome by the parameters of the game. It is important to remember that the LLN only applies (as the name indicates) when a large number of observations are considered. There is no principle that a small number of observations will coincide with the expected value or that a streak of one value will immediately be ""balanced"" by the others (see the gambler's fallacy)