# Independent standard normal variables

• Nov 30th 2009, 05:24 PM
tbl9301
Independent standard normal variables
Let X and Y be independent standard normal variables. Find:
a) P(3X + 2Y > 5)
b) P(min(X,Y) < 1)
c) P(|min(X,Y)| < 1)
d) P(min(X,Y) > max(X,Y) - 1)

I know this is probably pretty straight forward, but I'm not sure how to do these ... I know, for example, part a is N(0,13) , but how do you know what to look up in the table? Thanks!
• Nov 30th 2009, 06:12 PM
mr fantastic
Quote:

Originally Posted by tbl9301
Let X and Y be independent standard normal variables. Find:
a) P(3X + 2Y > 5)
b) P(min(X,Y) < 1)
c) P(|min(X,Y)| < 1)
d) P(min(X,Y) > max(X,Y) - 1)

I know this is probably pretty straight forward, but I'm not sure how to do these ... I know, for example, part a is N(0,13) , but how do you know what to look up in the table? Thanks!

You're expected to know that if X and Y are independent and X ~ Normal $\displaystyle (\mu_1, \sigma^2_1)$and Y ~ Normal $\displaystyle (\mu_2, \sigma^2_2)$ then $\displaystyle U = aX + bY$ ~ Normal $\displaystyle (\mu = a \mu_1 + b \mu_2, \sigma^2 = a^2 \sigma^2_1 + b^2 \sigma_2^2)$.
• Dec 1st 2009, 10:58 PM
matheagle
P(min(X,Y) < 1)=1-P(min(X,Y) > 1)=1-P(X>1,Y>1)=1-P(X>1)P(Y>1)