# Math Help - Expectancy (mean) of Probability density function composed of delta/rect function

1. ## Expectancy (mean) of Probability density function composed of delta/rect function

Conceptually I can work it out, but I'm not sure how to put it down mathematically. Since the functions are abstracted a bit. Could some one help write out how this should be done?

pdf : 0.5 delta(t) + 1/4 rect ((t-1)/2)

2. is this unifrom distribution

3. Not sure what you're asking, my graph is meant to show that there's a 50% of the random variable X being 0 and a 50% chance of being uniformly distributed between 0 and 2. I'm unsure how to deal with the dirac delta function when calculating the E[X]... Thanks in advance.

4. Originally Posted by T12
Conceptually I can work it out, but I'm not sure how to put it down mathematically. Since the functions are abstracted a bit. Could some one help write out how this should be done?

pdf : 0.5 delta(t) + 1/4 rect ((t-1)/2)

$\displaystyle \mu = 0 \cdot \frac{1}{2} + \int_0^2 \frac{t}{4} \, dt$

5. thank you, nice and simple. And sorry for wrong section. I put it there in terms of how simple it should be. Rather than whether pre university people have even heard of dirac delta functions.