Slide 1
... • probability model – formally, it gives you formulas to calculate probabilities, determine average outcomes, and figure the amount of variability in data • e.g. probability model helps you to determine the average number of times you need to play to win a lottery game • fundamental parts of probabi ...
... • probability model – formally, it gives you formulas to calculate probabilities, determine average outcomes, and figure the amount of variability in data • e.g. probability model helps you to determine the average number of times you need to play to win a lottery game • fundamental parts of probabi ...
Exercises L3: Probability Theory
... A cupboard has 3 drawers: in the first there are two golden coins, in the second one golden and one silver coin and in the third two silver coins. Somebody opens an arbitrary drawer and chooses an arbitrary coin: it is a golden coin. What is the probability that the second coin from this drawer is g ...
... A cupboard has 3 drawers: in the first there are two golden coins, in the second one golden and one silver coin and in the third two silver coins. Somebody opens an arbitrary drawer and chooses an arbitrary coin: it is a golden coin. What is the probability that the second coin from this drawer is g ...
CMSC 203 / 0202 Fall 2002
... Find the probability of each outcome when a biased die is rolled, if rolling a 2 or 4 are each three times as likely as rolling each of the other four numbers on the die. What is the probability of rolling a 7 with two ordinary dice? Exercise 4.5.5: Suppose a pair of dice is loaded. The probab ...
... Find the probability of each outcome when a biased die is rolled, if rolling a 2 or 4 are each three times as likely as rolling each of the other four numbers on the die. What is the probability of rolling a 7 with two ordinary dice? Exercise 4.5.5: Suppose a pair of dice is loaded. The probab ...
Practice problems
... 1. A number x is selected at random in the interval [−1, 1]. Consider the events A = {x < 0} and B = {|x − 0.5| < 1}. Find the probabilities of B, A ∩ B, and A ∪ B. 2. Section 2.2, # 9 3. Section 2.3, # 11. Also, what is the probability of at least two dice showing up with the same face, if only fiv ...
... 1. A number x is selected at random in the interval [−1, 1]. Consider the events A = {x < 0} and B = {|x − 0.5| < 1}. Find the probabilities of B, A ∩ B, and A ∪ B. 2. Section 2.2, # 9 3. Section 2.3, # 11. Also, what is the probability of at least two dice showing up with the same face, if only fiv ...
Notes on
... Vocabulary/Language of discipline Variable: a symbol, usually a letter, which stands for different quantities. Expression: a combination of variables and numbers representing a mathematical relationship. Function: rule that tells you how to perform one or more operations on a number, called the inpu ...
... Vocabulary/Language of discipline Variable: a symbol, usually a letter, which stands for different quantities. Expression: a combination of variables and numbers representing a mathematical relationship. Function: rule that tells you how to perform one or more operations on a number, called the inpu ...
skills summary - SAT
... (arithmetic mean) of a list of n numbers is equal to the sum of the numbers divided by n. For example, the mean of 2, 3, 5, 7, and 13 is ...
... (arithmetic mean) of a list of n numbers is equal to the sum of the numbers divided by n. For example, the mean of 2, 3, 5, 7, and 13 is ...
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)