Probability, expectation and standard deviation of binomial distribution

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Simon Thomas 6 years, 1 month ago

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Name	Status	Author	Last Modified
Probability, expectation and standard deviation of binomial distribution	draft	Simon Thomas	07/02/2019 10:25
Rachel's copy of Probability, expectation and standard deviation of binomial distribution	draft	Rachel Gargan	19/02/2019 12:02

Question statement

{pre} $\var{thismany}$ {post}

{something} $\var{number1}$ {else}

Give any introductory information the student needs.

			Name	Type	Generated Value

pre	string
descx1	string	number of chocolate chip cooki
something	string
thisnumber	integer	3
what	string	daily sales.
things	string	chocolate chip cookies.
descx	string	the number of chocolate chip c
tol	number	0.001
prob	rational	4/25
thisaswell	string	our selection contains no more
else	string	biscuits are selected at rando
thismany	integer	16
number1	integer	8
post	string	% of biscuits made by a baker
prob2	number	0.626
prob1	number	0.096
thatnumber	integer	1
this	string	our selection contains exactly
v	integer	0
tprob1	number	0.0959277825
tprob2	number	0.6255915347
sd	decimal	dec("1.037")

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
' '

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `string`

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
3. Gap Gap 2. Number entry
  Add
4. Gap Gap 3. Number entry
  Add
Part b) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

Assuming a binomial distribution for $X$ , {descX}, write down the values of $n$ and $p$.

$X \sim \operatorname{bin}(n,p)$

$n=\; $?Gap 0. $p=\;$?Gap 1.

Find $\operatorname{E}[X]$ the expected {descX1}

$\operatorname{E}[X]=$?Gap 2.

Find the standard deviation for the {descX1}

Standard deviation = ? Gap 3. (to 3 decimal places).

Advice

1. $X \sim \operatorname{bin}(\var{number1},\var{prob})$, so $n= \var{number1},\;\;p=\var{prob}$.

2. The expectation is given by $\operatorname{E}[X]=n\times p=\var{number1}\times \var{prob}=\var{number1*prob}$

3. $\operatorname{stdev}(X)=\sqrt{n\times p \times (1-p)}=\sqrt{\var{number1}\times \var{prob} \times \var{1-prob}}=\var{sd}$ to 3 decimal places.

1. \[ \begin{eqnarray*}\operatorname{P}(X = \var{thisnumber}) &=& \dbinom{\var{number1}}{\var{thisnumber}}\times\var{prob}^{\var{thisnumber}}\times(1-\var{prob})^{\var{number1-thisnumber}}\\& =& \var{comb(number1,thisnumber)} \times\var{prob}^{\var{thisnumber}}\times\var{1-prob}^{\var{number1-thisnumber}}\\&=&\var{prob1}\end{eqnarray*} \] to 3 decimal places.

\[ \begin{eqnarray*}\operatorname{P}(X \leq \var{thatnumber})& =& \simplify[all,!collectNumbers]{P(X = 0) + P(X = 1) + {v}*P(X = 2)}\\& =& \simplify[zeroFactor,zeroTerm,unitFactor]{{1 -prob} ^ {number1}+ {number1} *{prob} *{1 -prob} ^ {number1 -1} + {v} * ({number1} * {number1 -1}/2)* {prob} ^ 2 *( {1 -prob} ^ {number1 -2})}\\& =& \var{prob2}\end{eqnarray*} \]

to 3 decimal places.

Give a worked solution to the whole question.

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Part	Test	Passed?
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Probability, expectation and standard deviation of binomial distribution

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Simon Thomas 6 years, 1 month ago

Error in variable testing condition

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Generated value: `string`

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Gap-fill

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Error

Probability, expectation and standard deviation of binomial distribution

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Simon Thomas 6 years, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: string

Parts

Gap-fill

Generated value: `string`