Simplifying equation: E(y) = [1-(10-9p)]^2 + [10-[(10-9p)]^2

[stm93]

I'm trying to find the variance of the following problem (tried to set it out in table format)

u= (10-9p)
X values are 1 and 10

|(y-u)^2 | [1-(10-9p)]^2 | [10-(10-9p)]^2 |
| prob | p | 1-p |

the equation I need to solve and simplify is:

E(y) = [1-(10-9p)]^2 + [10-[(10-9p)]^2



In the answer book my teacher has given the simplified answer, which he has put as : 81(p-p^2)

I've not been able to get to that answer, can anyone body run me through in detail the steps to get to 81(p-p^2)?

I've got an exam on monday and this is one of the question types that Is going to appear

ANy help would be really appreciated!

 

[Deleted member 4993]

I'm trying to find the variance of the following problem (tried to set it out in table format)
u= (10-9p)
X values are 1 and 10
|(y-u)^2 | [1-(10-9p)]^2 | [10-(10-9p)]^2 |
| prob | p | 1-p |
the equation I need to solve and simplify is:
E(y) = [1-(10-9p)]^2 + [10-[(10-9p)]^2
In the answer book my teacher has given the simplified answer, which he has put as : 81(p-p^2)
I've not been able to get to that answer, can anyone body run me through in detail the steps to get to 81(p-p^2)?
I've got an exam on monday and this is one of the question types that Is going to appear
ANy help would be really appreciated!

E(y) = [1-(10-9p)]^2 + [10-[(10-9p)]^2 should simplify to 81 - 162*p + 162 *p^2 ......... EDITED
Please share your work with us - so that we can see where do\es the mistake\s lie.

 

[stm93]

E(y) = [1-(10-9p)]^2 + [10-[(10-9p)]^2 should simplify to 81(p-p^2).

Please share your work with us - so that we can see where do\es the mistake\s lie.

Thanks, I will show my workings out and hopefully you can show me where I am going wrong

First equation [1-(10-9p)]^2

1-(10-9p).... = (-9-9p)........ (-9-9p)^2 = 81-81p

(81-81p) x p = 81p -81p^2

Second equation [10-(10-9p)]^2
10-(10-9p) = -9p

-9p^2 = 81p

81p x (1-p)
= 81p - 81p^2

So we have 81p-81p^2 and 81p-81p^2

Clearly at this stage I have got this wrong, thats as far as I got, could you show the workings to get to 81(p-p^2) please?

many thanks

 

[Deleted member 4993]

Thanks, I will show my workings out and hopefully you can show me where I am going wrong

First equation [1-(10-9p)]^2

1-(10-9p).... = (-9-9p)........ (-9-9p)^2 = 81-81p .... Incorrect

Remember → (a + b)^2 = (a + b) * (a + b) = a^2 + b^2 + 2*a*b

so [1 - (10 - 9p)]^2 = [1 - 10 + 9p]^2 = [-9 + 9p]^2

= (-9)^2 + (-9p)^2 + 2 * (-9) * (9p)

= 81 + 81*p^2 - 162 *p ............................................edited (corrected sitting in the corner)

(81-81p) x p = 81p -81p^2

Second equation [10-(10-9p)]^2
10-(10-9p) = -9p

-9p^2 = 81p.... .... Incorrect

[10 -(10-9*p)]^2 = [10 - 10 + 9*p]^2 = [9*p]^2 = 81 * p^2

81p x (1-p)
= 81p - 81p^2

So we have 81p-81p^2 and 81p-81p^2

Clearly at this stage I have got this wrong, thats as far as I got, could you show the workings to get to 81(p-p^2) please?

many thanks

There was a mistake in my previous response ... please look at the corrected response.

Continue....

 

[stm93]

There was a mistake in my previous response ... please look at the corrected response.

Continue....

I've been able to work out how you got to 81+162*p+162*p^2

[1-(10-9p)]^2 = (-9+9p) * (-9+9p) = 81 - 162p + 81p^2

[10-(10-9p)]^2 = (-9p)*(-9p) = 81p^2

So we have 81 - 162*p + 162*p^2

Thanks for that bit!

But I dont see how that simplifies to 81(p-p^2)?

Is that a mistake by my teacher?

If not, could you explain how I get from 81 + 162*p + 162*p^2 to 81(p-p^2)?

many thanks

 

[Deleted member 4993]

I've been able to work out how you got to 81+162*p+162*p^2

[1-(10-9p)]^2 = (-9+9p) * (-9+9p) = 81 - 162p + 81p^2

[10-(10-9p)]^2 = (-9p)*(-9p) = 81p^2

So we have 81 - 162*p + 162*p^2

Thanks for that bit!

But I dont see how that simplifies to 81(p-p^2)?

Is that a mistake by my teacher?

If not, could you explain how I get from 81 + 162*p + 162*p^2 to 81(p-p^2)?

many thanks

I fixed some mistakes I had made - and you are correct that it does not reduce to the given answer.