# Find the p.d.f. and identify.

1. Jan 23, 2012

### thesandbox

1. The problem statement, all variables and given/known data

X1 ∼ N(μ112) and X2 ∼ N(μ222)

Let Y = X1 + X2

Find the p.d.f. of Y & label the distribution.

2. Relevant equations

3. The attempt at a solution

µY=E[Y]=E[X1+X2]=E[X1]+E[X2]=µ12

σY2=E[Y2] - µY2

E[X12+ 2X1X2 +X22] - (µ12)2

I think that might be how you start it. Feel free to correct me and start over or continue. Thanks.

2. Jan 24, 2012

### vela

Staff Emeritus
It's kind of hard to make suggestions without knowing more about what you know. What do you know about sums of random variables?

3. Jan 25, 2012

### thesandbox

Figured it out. The above doesn't account for all moments (rth)

MX1 + X2 = MX1(t)⋅MX2(t)

MXi=e$\mu$it + (1/2)σi2t2

Following N~($\mu$1 + $\mu$2 , σ12 + σ22)

Last edited: Jan 25, 2012