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RJLiberator
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Homework Statement
We have F(x) = ∑ (1/2)^j [Sum goes from j=1 to x]
For the cdf F(x), find the pmf f(x), the 25th percentile, and the 60th percentile.
Homework Equations
The Attempt at a Solution
I've been doing numerous of these for continuous distributions, however this one is tricking up my understanding.
So we have a CDF that is being summed here, but a CDF function can only go from 0 to 1.
So, would that mean that x mus equal 2, since 1/2 + 1/2 = 1?
Thus, the graph of F(x) just looks like 0 until it reaches 1, then it jumps up to 1/2 until it reaches x = 2 and stabilizes at 1.
Thus, the PDF is then 1/2 at x = 1 and 2, and 0 elsewhere.
Thus, the 25th percentile is 0.
The 60th percentile is x = 1 as it attains a value of 0.5 which is less than 0.6.
Do I have my understanding correct?