Binomial distribution

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Last updated 10:07 PM on 4/3/24
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11 Terms

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What is binomial distribution?

The probability of a number of successes in a finite set of trials

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How is the probability of the number of successes, X , given by?

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if we have n trials, each with a probability of success p

<p>LOOK AT PHOTO</p><p>if we have <mark data-color="green">n</mark> trials, each with a probability of success <mark data-color="red">p</mark></p>
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How do we display a binomial distribution?

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X is distributed binomially with n trials each having probability of success p


X~B(n,p)

<p>LOOK AT PHOTO</p><p><mark data-color="yellow">X</mark> is distributed binomially with <mark data-color="green">n trials</mark> each having <mark data-color="red">probability of success p</mark></p><p></p><p><mark data-color="red">X~B(n,p)</mark></p>
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<p>Example question </p><p>a) State the distribution of X, the number of heads in the 5 tosses</p>

Example question

a) State the distribution of X, the number of heads in the 5 tosses

X ~ B (5, 2/3 )

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<p>b) Find P(X= 1)</p>

b) Find P(X= 1)

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10/243

<p>LOOK AT PHOTO</p><p>10/243</p>
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<p>c) Find P (X=3)</p>

c) Find P (X=3)

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80/ 243

<p>LOOK AT PHOTO</p><p>80/ 243</p>
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What are the 4 conditions of binomial distribution? Assumptions, suggest a suitable model

You can model X with a binomial distribution, B(n,p) if:

  • there is a fixed number of trials, n

  • there are only 2 possible outcomes (success and failure)

  • there is a fixed probability of success, p

  • each trial is independent of all trials

<p>You can model X with a binomial distribution, B(n,p) if:</p><ul><li><p>there is a fixed number of trials, n</p></li><li><p>there are only 2 possible outcomes (success and failure)</p></li><li><p>there is a fixed probability of success, p</p></li><li><p>each trial is independent of all trials</p></li></ul>
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What is n sometimes called?

the index

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What is p sometimes called?

the parameter

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<p>Example 4</p>

Example 4

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<p>Example 5</p>

Example 5

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