# S1

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Yiuyu

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#1

A computer company provides an insurance policy for one of its systems. If the system fails during the first year, the policy pays £3,000; if it fails during the second year, the policy pays £2,000; and if it fails during the third year, the policy pays £1,000. The policy terminates after the first payout or after 3 years, whichever is the sooner. If the system has not failed at the beginning of a year, the probability that it will fail at some point during that year is 0.1. How much should the company charge for the insurance policy so that, on average, its net gain per policy is £100?

Well I did (0.1*3000) +.... +... and got =600

Well I did (0.1*3000) +.... +... and got =600

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ThomH97

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#2

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#2

Remember that to pay out £2,000, the system must have

**not**failed in the first year, and also failed in the second year. Similarly for the £1,000 in the third year.
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Yiuyu

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#3

(Original post by

Remember that to pay out £2,000, the system must have

**ThomH97**)Remember that to pay out £2,000, the system must have

**not**failed in the first year, and also failed in the second year. Similarly for the £1,000 in the third year.
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Yiuyu

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#4

**ThomH97**)

Remember that to pay out £2,000, the system must have

**not**failed in the first year, and also failed in the second year. Similarly for the £1,000 in the third year.

**not**failed in the first year which is 90% chance? So I get 180 pounds and for 1000 pounds I have got 81 pounds which gives me 561 in total , then I add 100?

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ThomH97

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#5

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#5

(Original post by

Okay to pay out 2000 the system must have

**Yiuyu**)Okay to pay out 2000 the system must have

**not**failed in the first year which is 90% chance? So I get 180 pounds and for 1000 pounds I have got 81 pounds which gives me 561 in total , then I add 100?
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#6

(Original post by

I'd agree with that

**ThomH97**)I'd agree with that

If X is geometrically distributed with p=0.8

where Y= X, X<3

or 2 otherwise

Find E(y)

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ThomH97

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#7

(Original post by

I have another question thanks

If X is geometrically distributed with p=0.8

where Y= X, X<3

or 2 otherwise

Find E(y)

**Yiuyu**)I have another question thanks

If X is geometrically distributed with p=0.8

where Y= X, X<3

or 2 otherwise

Find E(y)

Though I am a bit confused by 'Y=2 otherwise' since Y already inherits a probability for 2 from X. I would guess at just adding the remaining probability onto P(X=2).

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#8

(Original post by

What values can Y take? And with what probability?

Though I am a bit confused by 'Y=2 otherwise' since Y already inherits a probability for 2 from X. I would guess at just adding the remaining probability onto P(X=2).

**ThomH97**)What values can Y take? And with what probability?

Though I am a bit confused by 'Y=2 otherwise' since Y already inherits a probability for 2 from X. I would guess at just adding the remaining probability onto P(X=2).

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#9

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#9

(Original post by

Anything less than 2 with p=0.8?

**Yiuyu**)Anything less than 2 with p=0.8?

Then, because these won't all add to 1, stick the extra onto P(Y=2)

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#10

(Original post by

P(Y=a) = P(X=a) for a<3.

Then, because these won't all add to 1, stick the extra onto P(Y=2)

**ThomH97**)P(Y=a) = P(X=a) for a<3.

Then, because these won't all add to 1, stick the extra onto P(Y=2)

So for (X=0) p =0.8 , what eqn am I using again?

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#11

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#11

(Original post by

Yeah I meant less than or equal to 2?

So for (X=0) p =0.8 , what eqn am I using again?

**Yiuyu**)Yeah I meant less than or equal to 2?

So for (X=0) p =0.8 , what eqn am I using again?

(I am assuming you are using the geometric distribution that permits the variable to be 0)

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#12

(Original post by

P(X=a) = (1-p)^a p

(I am assuming you are using the geometric distribution that permits the variable to be 0)

**ThomH97**)P(X=a) = (1-p)^a p

(I am assuming you are using the geometric distribution that permits the variable to be 0)

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#13

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#13

(Original post by

But the answer is 1.2? So Idk how we could get that?

**Yiuyu**)But the answer is 1.2? So Idk how we could get that?

Weird question though, was there no other information?

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#14

(Original post by

In that case it's the 'other' geometric distribution, where the formula is P(X=a) = (1-p)^(a-1) p. I don't know which exam board you're doing, but this will be consistent within them.

Weird question though, was there no other information?

**ThomH97**)In that case it's the 'other' geometric distribution, where the formula is P(X=a) = (1-p)^(a-1) p. I don't know which exam board you're doing, but this will be consistent within them.

Weird question though, was there no other information?

Literally thats all they have gave me

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#15

(Original post by

But that unfortunately gives me an answer higher than 1.2?

Literally thats all they have gave me

**Yiuyu**)But that unfortunately gives me an answer higher than 1.2?

Literally thats all they have gave me

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#16

(Original post by

With the 'new' formula, what is P(Y=1)? Everything else goes into P(Y=2) because it's a weird question asking you to transform just one value. Then you can work out E(Y) in the usual way.

**ThomH97**)With the 'new' formula, what is P(Y=1)? Everything else goes into P(Y=2) because it's a weird question asking you to transform just one value. Then you can work out E(Y) in the usual way.

and P (Y=2) =0.16 right?

I get 0.96 for the total?

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#17

Then E(Y) gets to 1.2. Remember E(Z) = sum over all z (z times P(Z=z))

Forgive the notation XD

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#18

(Original post by

This is the weird bit that I'm guessing as to what they mean. You have 0.96 probability so far, so you need to add the remaining 0.04 to P(Y=2) to get 0.2.

Then E(Y) gets to 1.2. Remember E(Z) = sum over all z (z times P(Z=z))

Forgive the notation XD

**ThomH97**)This is the weird bit that I'm guessing as to what they mean. You have 0.96 probability so far, so you need to add the remaining 0.04 to P(Y=2) to get 0.2.

Then E(Y) gets to 1.2. Remember E(Z) = sum over all z (z times P(Z=z))

Forgive the notation XD

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#19

(Original post by

So I just randomly add 0.04? and where does the extra 0.2 come from again?

**Yiuyu**)So I just randomly add 0.04? and where does the extra 0.2 come from again?

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#20

(Original post by

They've restricted the values Y can take to be 1 and 2. You've found P(Y=1) from the geometric formula, so the remaining probability must all be for Y=2 (all probabilities sum to 1).

**ThomH97**)They've restricted the values Y can take to be 1 and 2. You've found P(Y=1) from the geometric formula, so the remaining probability must all be for Y=2 (all probabilities sum to 1).

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