# Calculating probabilitiesWatch

#1
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.
0
4 years ago
#2
|Y-3.5| > 1.5 means Y > 5 or Y < 2.
0
4 years ago
#3
(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)
0
#4
(Original post by DFranklin)
|Y-3.5| > 1.5 means Y > 5 or Y < 2.

(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?
0
4 years ago
#5
(Original post by Monaa123)

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)
0
4 years ago
#6
(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)
4 years ago
#7
(Original post by ghostwalker)
I think you meant:

W ~ N(5-6, 2+4x1)= N(-1,6)
you are correct
0
#8
(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!
1
4 years ago
#9
(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.
0
#10
(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
0
X

new posts
Latest
My Feed

### Oops, nobody has postedin the last few hours.

Why not re-start the conversation?

see more

### See more of what you like onThe Student Room

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

### University open days

• Cranfield University
Cranfield Forensic MSc Programme Open Day Postgraduate
Thu, 25 Apr '19
• University of the Arts London
Open day: MA Footwear and MA Fashion Artefact Postgraduate
Thu, 25 Apr '19
• Cardiff Metropolitan University
Sat, 27 Apr '19

### Poll

Join the discussion

#### Have you registered to vote?

Yes! (368)
37.28%
No - but I will (74)
7.5%
No - I don't want to (69)
6.99%
No - I can't vote (<18, not in UK, etc) (476)
48.23%