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Approximating a Binomial Distribution with a Normal Distribution

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Approximating a Binomial Distribution with a Normal Distribution

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1. Approximating a Binomial Distribution with a Normal Distribution The coin flipping example

A Discrete Probability Distribution: The Binomial Distribution

A Discrete Probability Distribution: The Binomial Distribution. MSIT 3000 Lecture 06. Objectives:. Recognize situations in which it is appropriate to use a binomial distribution. Be able to use the binomial distribution to calculate probabilities.

735 views • 15 slides

Normal Approximation to Binomial Distribution

Normal Approximation to Binomial Distribution. Consider the binomial distribution with n trials, and probability of success is p This distribution is approximately normal if np &gt; 5 and nq &gt; 5. In this case it is approximated by a normal distribution with Mean = np and Variance = npq.

868 views • 12 slides

Binomial Distribution

Binomial Distribution. A binomial experiment possesses the following properties 1 – a fixed number, n, of trials 2 – two outcomes for each trial 3 – constant probability of ‘success’ on each trial 4 – independence between any two trials . Binomial Random Variable.

671 views • 8 slides

Binomial Distribution Vs. Poisson Distribution

Binomial Distribution Vs. Poisson Distribution. Binomial Distribution Used to model the number of successes (i.e. the occurrence of an event) in a finite trials ( n trials) Each trial results in one of two possible outcomes (success or failure)

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Binomial Distribution

Binomial Distribution. Many companies view their individual outcomes as successes or failures. Repeated independent trials measured in terms of such successes or failures are Bernoulli trials.

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Binomial Distribution

Binomial Distribution. Memory trick. bi. no. mi. al. bi. Means two There are TWO possible outcomes Success or Failure. no. No. stands for number There are a fixed number of identical trials. Discrete – bar graph not histogram!. mi. Mi sounds like me. Me? I am dependent on no one!

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Normal Approximation to the Binomial Distribution

Normal Approximation to the Binomial Distribution. Objective. To understand and know how to calculate probabilities when asked to use a Normal approximation to the Binomial Distribution. To know the conditions under which this approximation can + should be used. Continuity Correction.

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Binomial distribution

Binomial distribution. Chapter 8. Binomial Setting. We use the acronym POTI P : Probability “ p ” same for every trial O : Outcome is either “success” or “failure” T : Trials are a fixed number “ n ” I : Each trial is independent of other trials. Binomial Formulas.

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Normal Approximation of the Binomial Distribution

Normal Approximation of the Binomial Distribution. 50. 30. What is the Probability of getting exactly 30 tails if a coin is tossed 50 times?. X = tails, x = 30 n = 50, p = 0.5. P(X = x) =. (0.5) 30 (1 – 0.5) 50 - 30. = 0.042. Find the probability that tails will occur less than 30 times….

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Binomial Distribution

Binomial Distribution. The binomial distribution is used when there are exactly two mutually exclusive outcomes of a trial. These trials are often referred to as Bernoulli trials E.g. Flipping a Coin (Head or Tail) Rolling a Dice – HUH ??????

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Binomial Distribution

Binomial Distribution. Discrete distribution Discrete random variable – dichotomous Yes/No, Dead/Alive, Success/Failure etc. Occurrence – Success (S) – Prob = p Non-occurrence – Failure (F) – Prob = 1-p= q Binomial Variable OR Bernoulli Variable

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Binomial Distribution

Binomial Distribution. Binomial Distribution The conditions for X to have a binomial distribution are There are only 2 possible outcomes: a success or a failure There is a fixed number of trials , n. The probability of success, p, at each individual trial is constant.

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Normal Distribution

Normal Distribution. Nojomi, MD, MPH Department of Community Medicine IUMS. Introduction. Parameters and Statistics Value or characteristic associated with population Is called : Parameter Value or characteristic calculated from a sample Is called : Statistics. Introduction.

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Binomial distribution

Binomial distribution. Nutan S. Mishra Department of Mathematics and Statistics University of South Alabama. Binomial experiment. An experiment is called binomial experiment if it satisfies following four conditions Consists of n trials All the trials are independent.

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Binomial Distribution

Probability. Binomial Distribution. topics covered. factorial calculations combinations Pascal’s Triangle Bin omial Distribu tion tables vs ca lculator inverting success and failure mean and variance. factorial calculations. n ! reads as “ n factorial”

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Binomial distribution

Binomial distribution. Use Cornell Notes. Setting For a binomial distribution. Acronym is POTI Probability needs to be the same for all trials Outcomes---there are only two—success or failure Trials—there is a set number of them Independent—each trial is independent from one another.

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Normal Approximation of the Binomial Distribution

Normal Approximation of the Binomial Distribution. N(0,1)  Bin. Example.

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Binomial Distribution

Binomial Distribution. Probability of Binary Events. Probability of success = p p(success) = p Probability of failure = q p(failure) = q p+q = 1 q = 1-p. Permutations &amp; Combinations 1. Suppose we flip a coin 2 times H H H T T H T T

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Binomial Distribution

Binomial Distribution. And general discrete probability distributions. Random Variable. A random variable assigns a number to a chance outcome or chance event. The definition of the random variable is denoted by uppercase letters at the end of alphabet, such as W, X, Y, Z.

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Binomial Distribution

Binomial Distribution. http://www.r-project.org/. Xijin Ge SDSU Math/Stat. All figures were generated using R . R is free yet powerful software for statistical computing. http://www.r-project.org/. Density function of binomial dist. n=30 p=0.5.

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Binomial Distribution

Binomial Distribution. Recall that for a binomial distribution, we must have:. Two possible outcomes, called success and failure. Constant probability. Independent trials. A fixed number of trials.

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