- #1
Bassalisk
- 947
- 2
Homework Statement
Random voltage is defined with its probability density function:
[tex] p_{\xi}(v)=2,25u(v+2)e^{-3(v+2)}+k\delta (v-2) [/tex]
u-Heaviside step function
a) Find constant k.
b) What is the probability of a random variable to take value of 2.
c) Find the cumulative distribution function.
Homework Equations
[itex]\int_{-\infty}^{+\infty}p_{\xi}(x)dx=1[/itex]
The Attempt at a Solution
I got that the constant k is 0,25. (if somebody would check that for me)
Now for the b), I am not sure. I know that when you have continuous distribution, probability that the function has 1 specific value is 0.
But this delta function at that point is confusing me. Does it change things? Should the probability be 0.25?
And I have troubles finding cumulative distribution. Help me out here.
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