This is interactive mathematicswhere you learn math by playing with it!homesitemapLiveMath infoFlash highlightsScientific Notebookmath blogaboutfeedback12. The Binomial Probability DistributionA binomial experiment is one that possesses the following properties:On this page...Mean and variance of a binomial distributionThe experiment consists of n repeated trials;Each trial results in an outcome that may be classified as a success or a failure (hence the name, binomial);The probability of a success, denoted by p, remains constant from trial to trial and repeated trials are independent.The number of successes X in n trials of a binomial experiment is called a binomial random variable.The probability distribution of the random variable X is called a binomial distribution, and is given by the formula:P(X) = Cnxpxqn−xwheren = the number of trialsx = 0, 1, 2, ... np = the probability of success in a single trialq = the probability of failure in a single trial(i.e. q = 1 − p)Cnx is a combinationP(X) gives the probability of successes in n binomial trials.Mean and Variance of Binomial DistributionIf p is the probability of success and q is the probability of failure in a binomial trial, then the expected number of successes in n trials (i.e. the mean value of the binomial distribution) isE(X) = μ = npThe variance of the binomial distribution isV(X) = σ2 = npqNote: In a binomial distribution, only 2 parameters, namely n and p, are needed to determine the probability.EXAMPLE 1Image sourceA die is tossed 3 times. What is the probability of(a) No fives turning up?(b) 1 five?(c) 3 fives?AnswerLoading...EXAMPLE 2Hospital records show that of patients suffering from a certain disease, 75% die of it. What is the probability that of 6 randomly selected patients, 4 will recover?AnswerLoading...EXAMPLE 3Image sourceIn the old days, there was a probability of 0.8 of success in any attempt to make a telephone call.Calculate the probability of having 7 successes in 10 attempts.AnswerLoading...EXAMPLE 4A (blindfolded) marksman finds that on the average he hits the target 4 times out of 5. If he fires 4 shots, what is the probability of(a) more than 2 hits?(b) at least 3 misses?AnswerLoading...EXAMPLE 5Image sourceThe ratio of boys to girls at birth in Singapore is quite high at 1.09:1.What proportion of Singapore families with exactly 6 children will have at least 3 boys? (Ignore the probability of multiple births.)[Interesting and disturbing trivia: In most countries the ratio of boys to girls is about 1.04:1, but in China it is 1.15:1.]AnswerLoading...EXAMPLE 6A manufacturer of metal pistons finds that on the average, 12% of his pistons are rejected because they are either oversize or undersize. What is the probability that a batch of 10 pistons will contain(a) no more than 2 rejects? (b) at least 2 rejects?AnswerLoading...11. Probability Distributions - Concepts13. Poisson Probability DistributionDidn't find what you are looking for on this page? Try search:The IntMath NewsletterSign up for the free IntMath Newsletter. Get math study tips, information, news and updates each fortnight. Join thousands of satisfied students, teachers and parents!Given name: * requiredFamily name:email: * requiredSee the Interactive Mathematics spam guarantee.Probability Lessons on DVDEasy to understand probability lessons on DVD. See samples before you commit.More info: Probability videosBookmark this pageAdd this page to diigo, Redditt, etc.Need a break? Play a math game. Well, they all involve math... No, really!Help keep Interactive Mathematics free!Home | Sitemap | About & Contact | Feedback & questions | Privacy | IntMath feed |Hello, PakistanPage last modified: 22 March 2007Valid HTML 4.01 | Valid CSSChapter ContentsCounting and Probability - Introduction1. Factorial Notation2. Basic Principles of Counting3. Permutations4. Combinations5. Introduction to Probability Theory6. Probability of an EventSingapore TOTOProbability and Poker7. Conditional Probability8. Independent and Dependent Events9. Mutually Exclusive Events10. Bayes' Theorem11. Probability Distributions - Concepts12. Binomial Probability Distributions13. Poisson Probability Distribution14. Normal Probability DistributionThe z-TableFollowing are the original SNB files (.tex or .rap) used in making this chapter. For more information, go to SNB info. SNB files1. Factorial Notation (SNB)2. Basic Principles of Counting (SNB)3. Permutations (SNB)4. Combinations (SNB)5. Introduction to Probability Theory (SNB)6. Probability of an Event (SNB)Singapore TOTO (SNB)Probability and Poker (SNB)7. Conditional Probability (SNB)8. Independent and Dependent Events (SNB)9. Mutually Exclusive Events (SNB)10. Bayes' Theorem (SNB)11. Probability Distributions - Concepts (SNB)12. Binomial Probability Distributions (SNB)13. Poisson Probability Distribution (SNB)14. Normal Probability Distribution (SNB)Comments, Questions?Math ApplicationsI get a good understanding of how math is applied to real world problems:In most lessonsIn some lessonsRarelyNeverVotes so far: 1570Follow IntMath on TwitterGet the Daily Math Tweet!IntMath on TwitterRecommendationEasy to understand probability lessons on DVD. Try before you commit. 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The Poisson distribution may be used when studying the number of events that occur in a given interval of time (or space). These events must occur at a constant rate, be independent of the time since the previous occurrence.
It is a polynomial if the square root is in a coefficient but not if it is applied to the variable. A polynomial can have only integer powers of the variable. Thus: sqrt(2)*x3 + 4*x + 3 is a polynomial expression but 2*x3 + 4*sqrt(x) + 3 is not.
z- statistics is applied under two conditions: 1. when the population standard deviation is known. 2. when the sample size is large. In the absence of the parameter sigma when we use its estimate s, the distribution of z remains no longer normal but changes to t distribution. this modification depends on the degrees of freedom available for the estimation of sigma or standard deviation. hope this will help u.... mona upreti.. :)
Suppose a set of observations for a variable X has a mean mx.If a scale factor of a is applied to the observations, and the origin is shifted to the left by a distance b, then the new mean will be (m/a)*x + b.
The answer depends on the context. In probability or statistics, when using a continuous distribution as an approximation for a discrete distribution it is advisable to use 0.5 as a "continuity correction". This is to allow for the fact that the discrete variable usually cannot take values between integers. In other situations a correction may be applied to allow for measurement error.
Yes, except that if you know that the distribution is uniform there is little point in using the empirical rule.
The p-value is the probability of any event or the level of significance for any statistical test. The z-score is a transformation applied to a Random Variable with any Normal distribution to the Standard Normal distribution.
Annals of Applied Probability was created in 1991.
Applied Probability Trust was created in 1964.
Yes. The normal distribution is used to approximate a binomial distribution when the sample size (n) times the probability of success (p), and the probability of failure (q) are both greater than or equal to 5. The mean of the normal approximation is n*p and the standard deviation is the square root of n*p*q.
application of probability in computer science
The probabilty can be applied to meiosis.
how theory of probability used in real life
Christopher G. Small has written: 'Hilbert space methods in probability and statistical inference' -- subject(s): Probabilities, Hilbert space, Mathematical statistics 'Functional Equations and How to Solve Them (Problem Books in Mathematics)' 'Expansions and Asymptotics for Statistics (Monographs on Statistics and Applied Probability)' -- subject(s): Asymptotic distribution (Probability theory), Asymptotic expansions
Each issue has a different ISBN.