Normal Distribution

• Feb 8th 2010, 01:04 PM
Dinkydoe
Normal Distribution
Given that $X,Y$ are independant Normal distributed variables, with $N(1,\sigma^2), \sigma = \frac{1}{2}$

How do I calculate $P(X+Y\leq t)$

I'm not quite sure how to calculate this since the cdf of the normal distribution doesn't have a closed form. And approximating with an error-function seems quite a bother. Any hints?
• Feb 8th 2010, 02:05 PM
matheagle
Let Z=X+Y, then $Z\sim N(E(Z), V(Z))$

you want $P(Z\le t)=\int_{-\infty}^t f_Z(z)dz$