Exponential distribution

[barabbas]

Hi, thankful if someone can help me out here.

Random variable Y is exponential distributed with expected value 2. Random variable X is equal to Y+(1/2) if 0≤Y≤2 and equals Y-(1/2) if 2<Y≤4. Otherwise X equals 0. What is the expected value of X?

I have a hard time with this one. I'm trying to use partial integration where I put in the value Y=2 and then add the calculations. So the first E[X] = x(5/2) with boundaries set to 0≤Y≤2 = 5. And the second integration for E[X] = x(3/2) with boundaries set to 2<Y≤4 = 9. Then E[X]= 5+9= 16

What am I missing?

 

[Romsek]

No idea what you're doing really but

[MATH]E[X] = \displaystyle \int_0^2 \left(y+\dfrac 1 2\right) \dfrac 1 2 e^{-y/2}~dy + \int_2^4 \left(y-\dfrac 1 2\right)\dfrac 1 2 e^{-y/2}~dy = \dfrac{-11+9 \sqrt{e}-9 e+5 e^2}{2 e^2} [/MATH]