Probability, expectation and variance of exponential distribution

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Simon Thomas 6 years, 2 months ago

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Question statement

The time, in {period} between {this} follows an exponential distribution with rate $\var{ra}$ i.e.

$X \sim \operatorname{exp}(\var{ra})$

Give any introductory information the student needs.

			Name	Type	Generated Value

that	string	two customers arriving
this	string	customer arrivals at the RyanJ
ans1	number	1.667
ans2	number	2.778
ans3	number	0.483
period	string	minutes
ra	number	0.6
tol	number	0.001
tans3	number	0.4831486655
thistime	number	1.1

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"two customers arriving "

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two customers arriving

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2. Gap Gap 1. Number entry
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Part b) Gap-fill
1. Gap Number entry
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Gap-fill

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Find $\operatorname{E}[X]$ between {this}:

$\operatorname{E}[X]=\;$ ?Gap 0.{period} (enter as a decimal correct to 3 decimal places).

Find $\operatorname{Var}(X)$ :

$\operatorname{Var}(X)=\;$ ?Gap 1.(enter as a decimal correct to 3 decimal places).

Advice

If $X \sim \operatorname{exp}(\lambda)$ then $\displaystyle \operatorname{E}[X] =\frac{1}{\lambda}$ and $\displaystyle \operatorname{Var}(X)=\frac{1}{\lambda^2}$ .

Also $P(X \lt a)=1-e^{-\lambda a}$ .

If $X \sim \operatorname{exp}(\var{ra})$ then:

$\displaystyle \operatorname{E}[X] =\frac{1}{\lambda}=\frac{1}{\var{ra}}=\var{ans1}$ to 3 decimal places.

$\displaystyle \operatorname{Var}(X) =\frac{1}{\lambda^2}=\frac{1}{\var{ra}^2}=\var{ans2}$ to 3 decimal places.

$P(X \lt \var{thistime}) = 1 -(e ^ {-\var{ ra} \times \var{thistime}}) = 1 -(e ^ { -\var{ra * thistime}}) = \var{ans3}$ to 3 decimal places.

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Probability, expectation and variance of exponential distribution

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Simon Thomas 6 years, 2 months ago

Error in variable testing condition

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Generated value: `string`

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Error

Probability, expectation and variance of exponential distribution

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Simon Thomas 6 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: string

Parts

Gap-fill

Generated value: `string`