Slide 1 - stat225
... 1. For Binomial, we know how many trials we have in total and for Geometric, we don’t know it, actually that number is not of interest. 2. For Binomial, there are usually several possibilities for a specific value of the variable, but for geometric, there is only one. (note: there is a coefficie ...
... 1. For Binomial, we know how many trials we have in total and for Geometric, we don’t know it, actually that number is not of interest. 2. For Binomial, there are usually several possibilities for a specific value of the variable, but for geometric, there is only one. (note: there is a coefficie ...
Example
... The instructor of a large class gives 15% each of A’s and D’s, 30% each of B’s and C’s, and 10% F’s. Choose a student at random from this class. The student’s grade on a 4-pt scale (A = 4) is a random variable X. Find the probability that the student got a B or better. ...
... The instructor of a large class gives 15% each of A’s and D’s, 30% each of B’s and C’s, and 10% F’s. Choose a student at random from this class. The student’s grade on a 4-pt scale (A = 4) is a random variable X. Find the probability that the student got a B or better. ...
here
... a. Estimate the probability distribution of the number of male children, say X, in these families using these data by calculating proportions. b. Find the expected value of X. c. Find the variance of X. d. Find the probability distribution of p̂ , where p̂ is the proportion of children in each famil ...
... a. Estimate the probability distribution of the number of male children, say X, in these families using these data by calculating proportions. b. Find the expected value of X. c. Find the variance of X. d. Find the probability distribution of p̂ , where p̂ is the proportion of children in each famil ...
homework 1
... 1) Assuming a Gaussian probability distribution answer the following questions (Use Tables in Taylor Appendix A and/or B): a) What is the probability of a value lying more than 1.5 from the mean? b) What is the probability of a value lying 1.5 above the mean? c) What is the probability of a valu ...
... 1) Assuming a Gaussian probability distribution answer the following questions (Use Tables in Taylor Appendix A and/or B): a) What is the probability of a value lying more than 1.5 from the mean? b) What is the probability of a value lying 1.5 above the mean? c) What is the probability of a valu ...
Chapter 7-8 Main Ideas • A random variable is a variable taking
... large population containing proportion p of successes. This is true as long as the sample size n is no more than 10% of the population size N. • The Normal approximation to the binomial distribution* says that if X is a count having the binomial distribution with parameters n and p, ...
... large population containing proportion p of successes. This is true as long as the sample size n is no more than 10% of the population size N. • The Normal approximation to the binomial distribution* says that if X is a count having the binomial distribution with parameters n and p, ...
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)