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 ...
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 ...
1 Math 1313 Expected Value Mean of a Data Set From the last
... From the last lesson, you should be familiar with random variables, and you should be able to construct a probability distribution for a random variable. In this lesson, you will learn how to compute the expected value of a probability distribution of a random variable. We begin with a familiar defi ...
... From the last lesson, you should be familiar with random variables, and you should be able to construct a probability distribution for a random variable. In this lesson, you will learn how to compute the expected value of a probability distribution of a random variable. We begin with a familiar defi ...
Chebyshev`s inequality Let X be a random variable taking
... Actually, this estimate is only meaningful for t > E[X]. We may also write it in the form E[X] ...
... Actually, this estimate is only meaningful for t > E[X]. We may also write it in the form E[X] ...
Law of large numbers
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)