Calculating probabilities Watch

Monaa123
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Calculate the following probabilities:

a) X~N(5,2), P(X>6)

b) Y~N(3.5,1), P(|Y - 3.5| > 1.5)

c) X~N(3,1), Y~N(5,2), X,Y independent; P(Y < 2X)

I've done part a, I got an answer of 0.2389. I'm not sure how to go about doing b or c.

I know that the answer for b should be 0.1336 and for c it should be 0.6591. I don't know how to work them out though.
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DFranklin
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|Y-3.5| > 1.5 means Y > 5 or Y < 2.
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TeeEm
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(Original post by Monaa123)
Calculate the following probabilities:

a) X~N(5,2), P(X>6)

b) Y~N(3.5,1), P(|Y - 3.5| > 1.5)

c) X~N(3,1), Y~N(5,2), X,Y independent; P(Y < 2X)

I've done part a, I got an answer of 0.2389. I'm not sure how to go about doing b or c.

I know that the answer for b should be 0.1336 and for c it should be 0.6591. I don't know how to work them out though.
for part (c)

form a new distribution W = Y - 2X

W ~ N(5-6, 1+4x2), i.e N(-1,9)

find P(w<0)
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Monaa123
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(Original post by DFranklin)
|Y-3.5| > 1.5 means Y > 5 or Y < 2.
Thanks, I got the answer!

(Original post by TeeEm)
for part (c)

form a new distribution W = Y - 2X

W ~ N(5-6, 1+4x2), i.e N(-1,9)

find P(w<0)
When you formed the new distribution, why did you do 1+4x2 for the second part?
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TeeEm
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(Original post by Monaa123)
Thanks, I got the answer!



When you formed the new distribution, why did you do 1+4x2 for the second part?
mean: E(aX +/- bY) = a E(X) +/- b E(Y)

variance: : Var(aX +/- bY) = a2 Var(X) + b2 Var(Y)
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ghostwalker
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(Original post by TeeEm)

form a new distribution W = Y - 2X

W ~ N(5-6, 1+4x2), i.e N(-1,9)
I think you meant:

W ~ N(5-6, 2+4x1)= N(-1,6)
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TeeEm
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(Original post by ghostwalker)
I think you meant:

W ~ N(5-6, 2+4x1)= N(-1,6)
you are correct
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Monaa123
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(Original post by TeeEm)
mean: E(aX +/- bY) = a E(X) +/- b E(Y)

variance: : Var(aX +/- bY) = a2 Var(X) + b2 Var(Y)
(Original post by ghostwalker)
I think you meant:

W ~ N(5-6, 2+4x1)= N(-1,6)

Thank you, I get it now!
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TeeEm
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(Original post by Monaa123)
Thank you, I get it now!
I hope you saw my last comment/correction

I typed very fast (I was teaching at that time) and I put the variance of X for Y and Y for X.

I hope I did not confuse you.
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Monaa123
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(Original post by TeeEm)
I hope you saw my last comment/correction

I typed very fast (I was teaching at that time) and I put the variance of X for Y and Y for X.

I hope I did not confuse you.
That's fine. I understood what you meant
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