#1 True or false: Even if the sample size is more than 1000‚ we cannot always use the normal approximation to binomial. Solution: If a sample is n>30‚ we can say that sample size is sufficiently large to assume normal approximation to binomial curve. Hence the statement is false. #2 A salesperson goes door-to-door in a residential area to demonstrate the use of a new Household appliance to potential customers. She has found from her years of experience that after demonstration‚ the
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Binomial‚ Bernoulli and Poisson Distributions The Binomial‚ Bernoulli and Poisson distributions are discrete probability distributions in which the values that might be observed are restricted to being within a pre-defined list of possible values. This list has either a finite number of members‚ or at most is countable. * Binomial distribution In many cases‚ it is appropriate to summarize a group of independent observations by the number of observations in the group that represent one of
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A useful distribution for fitting discrete data: revival of the Conway–Maxwell–Poisson distribution Galit Shmueli‚ University of Maryland‚ College Park‚ USA Thomas P. Minka and Joseph B. Kadane‚ Carnegie Mellon University‚ Pittsburgh‚ USA Sharad Borle Rice University‚ Houston‚ USA and Peter Boatwright Carnegie Mellon University‚ Pittsburgh‚ USA [Received June 2003. Revised December 2003] Summary. A useful discrete distribution (the Conway–Maxwell–Poisson distribution) is revived
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BINOMIAL THEOREM OBJECTIVES Recognize patterns in binomial expansions. Evaluate a binomial coefficient. Expand a binomial raised to a power. Find a particular term in a binomial expansion Understand the principle of mathematical induction. Prove statements using mathematical induction. Definition: BINOMIAL THEOREM Patterns in Binomial Expansions A number of patterns‚ as follows‚ begin to appear when we write the binomial expansion of a b n‚ where n is a positive integer
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Binomial nomenclature (also called binominal nomenclature or binary nomenclature) is a formal system of naming species of living things by giving each a name composed of two parts‚ both of which use Latin grammatical forms‚ although they can be based on words from other languages. Such a name is called a binomial name (which may be shortened to just "binomial")‚ a binomen or a scientific name; more informally it is also called a Latin name. The first part of the name identifies the genus to which
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The binomial theorem is a simplified way of finding the expansion of a binomial to a certain power. We can of course find the expanded form of any binomial to a certain power by writing it and doing each step‚ but this process can be very time consuming when you get into let’s say a binomial to the 10th power. Example: (x+y)^0=1 of course because anything to the power if 0 equal 1 (x+y)^1= x+y anything to a power of 1 is just itself. (x+y)^2= (x+y)(x+y) NOT x^2+y^2. So expand (x+y)(x+y)=x^2+xy+yx+y^2
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The Binomial Distribution October 20‚ 2010 The Binomial Distribution Bernoulli Trials Definition A Bernoulli trial is a random experiment in which there are only two possible outcomes - success and failure. 1 Tossing a coin and considering heads as success and tails as failure. The Binomial Distribution Bernoulli Trials Definition A Bernoulli trial is a random experiment in which there are only two possible outcomes - success and failure. 1 Tossing a coin and considering
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BINOMIAL THEOREM : AKSHAY MISHRA XI A ‚ K V 2 ‚ GWALIOR In elementary algebra‚ the binomial theorem describes the algebraic expansion of powers of a binomial. According to the theorem‚ it is possible to expand the power (x + y)n into a sum involving terms of the form axbyc‚ where the coefficient of each term is a positive integer‚ and the sum of the exponents of x and y in each term is n. For example: The coefficients appearing in the binomial expansion are known as binomial coefficients.
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expected average outcome over many observations.The common symbol for the mean (also known as the expected value of X) is ‚ formally defined by Variance - The variance of a discrete random variable X measures the spread‚ or variability‚ of the distribution‚ and is defined by The standard deviation is the square root of the variance. Expectation - The expected value (or mean) of X‚ where X is a discrete random variable‚ is a weighted average of the possible values that X can take‚ each value
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Poisson distribution is a discrete distribution. It is often used as a model for the number of events (such as the number of telephone calls at a business‚ number of customers in waiting lines‚ number of defects in a given surface area‚ airplane arrivals‚ or the number of accidents at an intersection) in a specific time period. It is also useful in ecological studies‚ e.g.‚ to model the number of prairie dogs found in a square mile of prairie. The major difference between Poisson and Binomial distributions
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