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picture1_Binomial Distribution Ppt 69388 | Chapter 8


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File: Binomial Distribution Ppt 69388 | Chapter 8
8 1 the binomial distribution a binomial experiment is a statistical experiment that has the following properties 1 the experiment consists of n repeated trials 2 each trial can result ...

icon picture PPTX Filetype Power Point PPTX | Posted on 29 Aug 2022 | 3 years ago
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                8.1 The Binomial 
                Distribution
                A binomial experiment is a statistical experiment 
                   that has the following properties: 
                   1.   The experiment consists of n repeated trials. 
                   2.   Each trial can result in just two possible outcomes. We 
                        call one of these outcomes a success and the other, a 
                        failure. 
                   3.   The probability of success, denoted by P, is the same 
                        on every trial. 
                   4.   The trials are independent; that is, the outcome on one 
                        trial does not affect the outcome on other trials.
                Discrete random variables only
                Example
                 Consider the following statistical experiment. You flip a 
                   coin 2 times and count the number of times the coin 
                   lands on heads. This is a binomial experiment because: 
                    1.  The experiment consists of repeated trials. We flip a coin 
                        2 times. 
                    2.  Each trial can result in just two possible outcomes - 
                        heads or tails. 
                    3.  The probability of success is constant - 0.5 on every trial. 
                    4.  The trials are independent; that is, getting heads on one 
                        trial does not affect whether we get heads on other trials.
       Notation
       x: The number of successes that result from the 
        binomial experiment. 
       n: The number of trials in the binomial experiment. 
       P: The probability of success on an individual trial. 
       Q: The probability of failure on an individual trial. 
        (This is equal to 1 - P.) 
       b(x; n, P): Binomial probability - the probability that 
        an n-trial binomial experiment results in exactly x 
        successes, when the probability of success on an 
        individual trial is P. 
                  Binomial or not?
          Tossing 20 coins and counting the number of heads.
             Yes
                 1.   Success is a heads, failure is a tails. 
                 2.   n = 20. 
                 3.   Independence is true – coins have no influence on each other. 
                 4.   p = 0.5 so X is B(20, .5). The possible values of X are the integers from 0 to 20.
          Picking 5 cards from a standard deck and counting the number of 
             hearts. We replace the card each time and reshuffle.
             Yes
                 1.   Success is a heart, failure is anything but a heart. 
                 2.   n = 5. 
                 3.   Independence is true. 
                 4.   p =.025 so X is B(5, .25). The possible values of X are the integers from 0 to 5.
          Picking 5 cards from a standard deck and counting the 
            number of hearts without replacing after each pick.
            No, b/c of independence issue
          Choosing a card from a standard deck until you get a 
            heart.
            No, b/c there are not a fixed number of observations
          It is estimated that 87% of computers users use 
            Explorer as their default web browser. We choose 50 
            computer users and ask their default browser.
            Yes – 
               1. Success is Explorer, failure is anything else. 
               2. n =50. 
               3. Independence seems logical. 
               4. p = 0.87 so X is B(50, .87). The possible values of X are 
                  the integers from 0 to 50.
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...The binomial distribution a experiment is statistical that has following properties consists of n repeated trials each trial can result in just two possible outcomes we call one these success and other failure probability denoted by p same on every are independent outcome does not affect discrete random variables only example consider you flip coin times count number lands heads this because or tails constant getting whether get notation x successes from an individual q equal to b results exactly when tossing coins counting yes independence true have no influence so values integers picking cards standard deck hearts replace card time reshuffle heart anything but without replacing after pick c issue choosing until there fixed observations it estimated computers users use explorer as their default web browser choose computer ask else seems logical...

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