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I have this table:

x    |     0     1     2     3     4     5
f(x) |    .7    .2   .05   .03   .01   .01
F(x) |    .7    .9   .95   .98   .99     1

Where f(x) is the density function for x and F(x) is the cumulative distribution function for x.

And I am being asked to use F to verify that P[X=3]=0.03

My guess is that I should start with P[X=3]=F(2) ... something ... something, since F(x)=P(X<=x) but I am not sure.

Any suggestions?

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up vote 2 down vote accepted

The CDF $F(x)$ is the sum of the probabilities $f(y)$ for $y \leq x$. Since $F(x+1) - F(x) = f(x+1)$, you can verify that $0.98 - 0.95 = 0.3$.

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cool, thanks :) – Mickel Nov 6 '10 at 18:56

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