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 probability of purchase (long run average) is 0.30. To perform
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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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Chapter 3 Probability Distributions 1. Based on recent records‚ the manager of a car painting center has determined the following probability distribution for the number of customers per day. Suppose the center has the capacity to serve two customers per day. |x |P(X = x) | |0 |0.05 | |1 |0.20 | |2 |0.30 | |3 |0.25 | |4 |0.15 | |5 |0.05 | a. What is the probability that one
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_____ 1. What is mean‚ variance and expectations? Mean - The mean of a discrete random variable X is a weighted average of the possible values that the random variable can take. Unlike the sample mean of a group of observations‚ which gives each observation equal weight‚ the mean of a random variable weights each outcome xi according to its probability‚ pi. The mean also of a random variable provides the long-run average of the variable‚ or the expected average outcome over many observations
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Probability distribution Definition with example: The total set of all the probabilities of a random variable to attain all the possible values. Let me give an example. We toss a coin 3 times and try to find what the probability of obtaining head is? Here the event of getting head is known as the random variable. Now what are the possible values of the random variable‚ i.e. what is the possible number of times that head might occur? It is 0 (head never occurs)‚ 1 (head occurs once out of 2 tosses)
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Math 107 002 Homework 5 (due 13 Oct 2011) Fall 2011 Please use your calculators and give your final answers to 3 significant figures. Show your work for full credit. Please state clearly all assumptions made. 1. Classify each random variable as discrete or continuous. (a) The number of visitors to the Museum of Science in Boston on a randomly selected day. (b) The camber-angle adjustment necessary for a front-end alignment. (c) The total number of pixels in a photograph produced by a digital camera
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8.1 BINOMIAL SETTING? In each situation below‚ is it reasonable to use a binomial distribution for the random variable X? Give reasons for your answer in each case. (a) An auto manufacturer chooses one car from each hour’s production for a detailed quality inspection. One variable recorded is the count X of finish defects (dimples‚ ripples‚ etc.) in the car’s paint. No: There is no fixed n (i.e.‚ there is no definite upper limit on the number of defects). (b) The pool of potential jurors for
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Probability Distribution Essay Example Suppose you flip a coin two times. This simple statistical experiment can have four possible outcomes: HH‚ HT‚ TH‚ and TT. Now‚ let the random variable X represent the number of Heads that result from this experiment. The random variable X can only take on the values 0‚ 1‚ or 2‚ so it is a discrete random variable Binomial Probability Function: it is a discrete distribution. The distribution is done when the results are not ranged along a wide range‚ but are
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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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The Poisson probability distribution‚ named after the French mathematician Siméon-Denis. Poisson is another important probability distribution of a discrete random variable that has a large number of applications. Suppose a washing machine in a Laundromat breaks down an average of three times a month. We may want to find the probability of exactly two breakdowns during the next month. This is an example of a Poisson probability distribution problem. Each breakdown is called an occurrence in Poisson
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