AP STATS – Chapter 8 Binomial vs. Geometric Probabilities Name 1
... iv. She gets exactly 4 bull’s-eyes. v. She gets at least 4 bull’s-eyes. vi. She gets at most 4 bull’s-eyes. e) How many bull’s-eyes do you expect her to get? ...
... iv. She gets exactly 4 bull’s-eyes. v. She gets at least 4 bull’s-eyes. vi. She gets at most 4 bull’s-eyes. e) How many bull’s-eyes do you expect her to get? ...
The Bernoulli Random Variable • Suppose a random experiment
... • We can use the Poisson distribution as an approximation to calculate binomial probabilities when n is large and p is small. The parameter of the Poisson would be λ = np. ...
... • We can use the Poisson distribution as an approximation to calculate binomial probabilities when n is large and p is small. The parameter of the Poisson would be λ = np. ...
3.3 Sampling Design
... Bias: systematic error, in favoring some parts of the population over others. Voluntary Response Sample: consists of people who choose themselves by responding to a general appeal. It’s biased because people with strong opinions, especially negative opinions, are most likely to respond. Sample desig ...
... Bias: systematic error, in favoring some parts of the population over others. Voluntary Response Sample: consists of people who choose themselves by responding to a general appeal. It’s biased because people with strong opinions, especially negative opinions, are most likely to respond. Sample desig ...
Lecture 2
... Let us build up our intuition starting with discrete random variables. Roll two “independent” fair dice. (We haven’t yet defined independence for random variables but just use your intuition.) Let X be the number shown on the first die, Y on the second and Z their sum. (Note that all three random va ...
... Let us build up our intuition starting with discrete random variables. Roll two “independent” fair dice. (We haven’t yet defined independence for random variables but just use your intuition.) Let X be the number shown on the first die, Y on the second and Z their sum. (Note that all three random va ...
+ Discrete Random Variables
... The probabilities pi must satisfy two requirements: 1. Every probability pi is a number between 0 and 1. 2. The sum of the probabilities is 1. To find the probability of any event, add the probabilities pi of the particular values xi that make up the event. ...
... The probabilities pi must satisfy two requirements: 1. Every probability pi is a number between 0 and 1. 2. The sum of the probabilities is 1. To find the probability of any event, add the probabilities pi of the particular values xi that make up the event. ...
Random Graphs
... Directed versions of the models we’ve discussed also exist. Weighted random graphs can be generated by, for instance, choosing a distribution besides Bernoulli for each edge independently. Instead of probabilistically choosing edges from G (n, p), we could choose from some geometric lattice or the g ...
... Directed versions of the models we’ve discussed also exist. Weighted random graphs can be generated by, for instance, choosing a distribution besides Bernoulli for each edge independently. Instead of probabilistically choosing edges from G (n, p), we could choose from some geometric lattice or the g ...
Randomness
Randomness is the lack of pattern or predictability in events. A random sequence of events, symbols or steps has no order and does not follow an intelligible pattern or combination. Individual random events are by definition unpredictable, but in many cases the frequency of different outcomes over a large number of events (or ""trials"") is predictable. For example, when throwing two dice, the outcome of any particular roll is unpredictable, but a sum of 7 will occur twice as often as 4. In this view, randomness is a measure of uncertainty of an outcome, rather than haphazardness, and applies to concepts of chance, probability, and information entropy.The fields of mathematics, probability, and statistics use formal definitions of randomness. In statistics, a random variable is an assignment of a numerical value to each possible outcome of an event space. This association facilitates the identification and the calculation of probabilities of the events. Random variables can appear in random sequences. A random process is a sequence of random variables whose outcomes do not follow a deterministic pattern, but follow an evolution described by probability distributions. These and other constructs are extremely useful in probability theory and the various applications of randomness.Randomness is most often used in statistics to signify well-defined statistical properties. Monte Carlo methods, which rely on random input (such as from random number generators or pseudorandom number generators), are important techniques in science, as, for instance, in computational science. By analogy, quasi-Monte Carlo methods use quasirandom number generators.Random selection is a method of selecting items (often called units) from a population where the probability of choosing a specific item is the proportion of those items in the population. For example, with a bowl containing just 10 red marbles and 90 blue marbles, a random selection mechanism would choose a red marble with probability 1/10. Note that a random selection mechanism that selected 10 marbles from this bowl would not necessarily result in 1 red and 9 blue. In situations where a population consists of items that are distinguishable, a random selection mechanism requires equal probabilities for any item to be chosen. That is, if the selection process is such that each member of a population, of say research subjects, has the same probability of being chosen then we can say the selection process is random.