Probability, S2, Var(X(8-X)) ? Watch

Infinity_Kev
Badges: 0
Rep:
?
#1
Report Thread starter 13 years ago
#1
X~U(3,7)

Y=X(8-X)

Finding E(Y) is ok and comes to 41/3.

How would you find Var(Y) ?

i tried E(Y²)=E([8X-X]²) and then using Var(Y)=E(X²)-E(X)² but that came out wrong.

book says answer is 3/4.
0
quote
reply
mikeyT
Badges: 2
Rep:
?
#2
Report 13 years ago
#2
(Original post by Infinity_Kev)

i tried E(Y²)=E([8X-X]²) and then using Var(Y)=E(X²)-E(X)² but that came out wrong.
should E(Y²)=E([8X-X²]²)? so you've just missed a square on the second X
0
quote
reply
Infinity_Kev
Badges: 0
Rep:
?
#3
Report Thread starter 13 years ago
#3
Yeah i did that acctually and got


E(Y²)=64X²-16X³+X^4

I might have made a mistake somewhere i think il go through it again.
0
quote
reply
Infinity_Kev
Badges: 0
Rep:
?
#4
Report Thread starter 13 years ago
#4
E(Y)=8*5 - \frac{1}{4} 

\int_3^7 x^2 dx

comes to \frac{41}{3}



now E(Y²) = E([8X-X²]²) = 64E(X²) - 16E(X³) + X^4

=\frac{64}{4} \int_3^7 x^2 dx

- \frac{16}{4} \int_3^7 x^3 dx

+ \frac{1}{4} \int_3^7 x^4 dx

which comes to \frac{2903}{15}

so Var(Y)=  \frac{2903}{15} - (\frac{41}{3})^2 = 6.7555...

the book says answer is  \frac{3}{4} can anyone spot a mistake?????
0
quote
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

University open days

  • University of Buckingham
    Psychology Taster Tutorial Undergraduate
    Fri, 14 Dec '18
  • University of Lincoln
    Mini Open Day at the Brayford Campus Undergraduate
    Wed, 19 Dec '18
  • University of East Anglia
    UEA Mini Open Day Undergraduate
    Fri, 4 Jan '19

Were you ever put in isolation at school?

Yes (134)
27.29%
No (357)
72.71%

Watched Threads

View All