Find the probability from the expected value?

[kylebutler]

Homework Statement

z = 2, P(Z=z)=1/6

z = 3, P(Z=z)=1/6

z = 5, P(Z=z)=1/6

z = 7, P(Z=z)= x

z = 11, P(Z=z)= y

I'm supposed to find x and y given that E(Z)= 5+2/3

I have no idea how to do this. All I got is 7x+11x=4 but I can't solve this

 

[LCKurtz]

Homework Statement

z = 2, P(Z=z)=1/6

z = 3, P(Z=z)=1/6

z = 5, P(Z=z)=1/6

z = 7, P(Z=z)= x

z = 11, P(Z=z)= y

I'm supposed to find x and y given that E(Z)= 5+2/3

I have no idea how to do this. All I got is 7x+11x=4 but I can't solve this

I think you mean you got 7x+11y = 4. To get another equation remember that the Z probabilities must add to 1.

 

[kylebutler]

I think you mean you got 7x+11y = 4. To get another equation remember that the Z probabilities must add to 1.

Thanks A LOT! How did I not think of that? :-)