Binomial Distribution
To understand binomial distributions and binomial probability, it helps to understand binomial experiments and some associated notation; so we cover those topics first. Binomial Experiment A binomial experiment (also known as a Bernoulli trial) is a statistical experiment that has the following properties: The experiment consists of n repeated trials. Consider the following statistical experiment. The experiment consists of repeated trials. Notation The following notation is helpful, when we talk about binomial probability. x: The number of successes that result from the binomial experiment. n: The number of trials in the binomial experiment. Binomial Distribution A binomial random variable is the number of successes x in n repeated trials of a binomial experiment. Suppose we flip a coin two times and count the number of heads (successes). The binomial distribution has the following properties: The mean of the distribution (μx) is equal to n * P . Binomial Formula and Binomial Probability
The normalcdf( Command - TI-Basic Developer
Command Summary Finds the probability for an interval of the normal curve. Command Syntax normalcdf(lower, upper [, μ, σ]) Menu Location Press: 2ND DISTR to access the distribution menu2 to select normalcdf(, or use arrows. Calculator Compatibility Token Size 2 bytes normalcdf( is the normal (Gaussian) cumulative density function. There are two ways to use normalcdf(. for the standard normal distribution :normalcdf(-1,1 for the normal distribution with mean 10 and std. dev. 2.5 :normalcdf(5,15,10,2.5 Often, you want to find a "tail probability" - a special case for which the interval has no lower or no upper bound. The normal distribution is often used to approximate the binomial distribution when there are a lot of trials. :binompdf(N,P,X can be :normalcdf(X-.5,X+.5,NP,√(NP(1-P :binomcdf(N,P,X,Y can be :normalcdf(X-.5,Y+.5,NP,√(NP(1-P As with other continuous distributions, any probability is an integral of the probability density function. or in terms of the error function:
Liar paradox
In philosophy and logic, the liar paradox or liar's paradox (pseudómenos lógos--ψευδόμενος λόγος—in Ancient Greek) is the statement "this sentence is false." Trying to assign to this statement a classical binary truth value leads to a contradiction (see paradox). If "This sentence is false." is true, then the sentence is false, but then if "This sentence is false." is false, then the sentence is true, and so on. History[edit] The Epimenides paradox (circa 600 BC) has been suggested as an example of the liar paradox, but they are not logically equivalent. One version of the liar paradox is attributed to the Greek philosopher Eubulides of Miletus who lived in the 4th century BC. The paradox was once discussed by St. "I said in my alarm, 'Every man is a liar!' In early Islamic tradition liar paradox was discussed for at least five centuries starting from late 9th century apparently without being influenced by any other tradition. Explanation of the paradox and variants[edit] E2 is false.
Boolean algebra
Boolean algebra was introduced by George Boole in his first book The Mathematical Analysis of Logic (1847), and set forth more fully in his An Investigation of the Laws of Thought (1854).[1] According to Huntington the term "Boolean algebra" was first suggested by Sheffer in 1913.[2] Boolean algebra has been fundamental in the development of digital electronics, and is provided for in all modern programming languages. It is also used in set theory and statistics.[3] History[edit] In the 1930s, while studying switching circuits, Claude Shannon observed that one could also apply the rules of Boole's algebra in this setting, and he introduced switching algebra as a way to analyze and design circuits by algebraic means in terms of logic gates. Values[edit] As with elementary algebra, the purely equational part of the theory may be developed without considering explicit values for the variables.[12] Operations[edit] Basic operations[edit] The basic operations of Boolean algebra are as follows. J.
'Truth or Lies' Brain Teaser
Truth or Lies Logic puzzles require you to think. You will have to be logical in your reasoning. You are traveling down a path and come to a fork in the road. Answer You point to either path and say, "Are you from this village?" Back to Top
