Calculate expectation and a probability from a frequency table, , ,

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Newcastle University Mathematics and Statistics 9 years, 2 months ago

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Question statement

The probabilities that {idef} {thing} will receive {episodes} per {period} about its {activity} are given by the following table:

Complaints	{values[0]}	{values[1]}	{values[2]}	{values[3]}	{values[4]}	{values[5]}	{values[6]}	{values[7]}	{values[8]}
Probability	{probabilities[0]}	{probabilities[1]}	{probabilities[2]}	{probabilities[3]}	{probabilities[4]}	{probabilities[5]}	{probabilities[6]}	{probabilities[7]}	{probabilities[8]}

Answer the following two parts, giving your answers to $2$ decimal places.

Give any introductory information the student needs.

			Name	Type	Generated Value

idef	string	an
thing	string	airline
episodes	string	complaints
period	string	day
activity	string	luggage handling

			Name	Type	Generated Value

p0	decimal	dec("5")
p1	decimal	dec("10")
p2	decimal	dec("15")
p3	decimal	dec("18")
p4	decimal	dec("28")
p5	decimal	dec("9")
p6	decimal	dec("7")
p7	decimal	dec("5")
p8	decimal	dec("3")
probabilities	list	List of 9 items
values	list	[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]

			Name	Type	Generated Value

r	integer	48
s	decimal	dec("5")
t	integer	52
t1	decimal	dec("5")
t2	decimal	dec("5")
u1	decimal	dec("2")
u2	decimal	dec("2")
u3	decimal	dec("2")
d	decimal	dec("3")

			Name	Type	Generated Value

expected_number	number	3.52
expect_int	integer	3
probexceed	number	0.52

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Statement

Parts

Part a) Gap-fill
1. Gap Number entry
  Add
Part b) Gap-fill
1. Gap Number entry
  Add

Gap-fill

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Find the expected number of {episodes} per {period}.

Expected number = Unnamed gap

Advice

a)

The expected number of {episodes} is given by:

\[ \simplify[]{{probabilities[0]}*{values[0]} + {probabilities[1]}*{values[1]} + {probabilities[2]}*{values[2]} + {probabilities[3]}*{values[3]} + {probabilities[4]}*{values[4]} + {probabilities[5]}*{values[5]} + {probabilities[6]}*{values[6]} + {probabilities[7]}*{values[7]} + {probabilities[8]}*{values[8]}} = \var{expected_number} \]

b)

We want the probability that the number of {episodes} exceeds $\var{expected_number}$.

Since the number of {episodes} is a whole number, this is the same as the probability that the number is $\var{expect_int+1}$ or more and is

\[\sum_{i=\var{expect_int+1}}^{i=8} \left( \text{Probability}(\var{episodes} = i ) \right)= \simplify[zeroTerm]{ {if(expect_int<1,probabilities[1],0)} + {if(expect_int<2,probabilities[2],0)} + {if(expect_int<3,probabilities[3],0)} + {if(expect_int<4,probabilities[4],0)} + {if(expect_int<5,probabilities[5],0)} + {if(expect_int<6,probabilities[6],0)} + {if(expect_int<7,probabilities[7],0)} + {if(expect_int<8,probabilities[8],0)}} = \var{probexceed}\]

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Calculate expectation and a probability from a frequency table, , ,

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Norah Storey 4 years, 1 month ago

Newcastle University Mathematics and Statistics 9 years, 2 months ago

Error in variable testing condition

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Generated value: `string`

Parts

Gap-fill

a)

b)

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Calculate expectation and a probability from a frequency table, , ,

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Norah Storey 4 years, 1 month ago

Newcastle University Mathematics and Statistics 9 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: string

Parts

Gap-fill

a)

b)

Generated value: `string`