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$p(x)=\frac{1}{9}(x-1)$, $x=2,3,4,5$. Why can this function not be a p.m.f?

$f(x)=\frac{2}{3}(x-3)$, $2\leq x\leq5$ Why can this function not be a p.d.f?

1 Answers 1

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Hint

Is the total mass or probability $1$ in each case; and are the functions non-negative?

In case $1$, is it true that $\sum_{i=2}^5p(x)\overset{?}{=}1$

In case $2$, is it true that $\int_2^5f(x)\,\mathrm{d}x\overset{?}=1$

$p(x)$ is not a probability mass function and $f(x)$ is not a probability density function.

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    Far too late at night for this.. sorry for the silly arithmetic mistake! :) x2012-05-03