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$A$ is absolutely continuous random variable. Given a density function $fa(a)$ I have to calculate $P(A = \frac 34)$.

I tried to just calculate the integral with both lower and upper limit $\frac 34$ and then $f(a)$ da but that just gives zero. What would be correct to do?

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Andrew C
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    Why do you think $0$ is wrong? – Arthur Mar 27 '17 at 08:20
  • It is the correct way to calculate it? – Andrew C Mar 27 '17 at 08:22
  • I would say it is, but technically it depends on your teacher. You could reason for it by saying that $P(A = 3/4) = P(3/4\leq A\leq 3/4)$, where the latter clearly justifies integrating the density function (or using the CDF), precicely because the distribution is continuous. – Arthur Mar 27 '17 at 08:23

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You are correct.

If $dF/dx = f$ then $$P(p \le X \le q) =\int_{p}^{q}f(x)\,dx=\left[F(x)\right]_{p}^{q}=F(q)-F(p)$$ If $p=q$ then this equals zero ($p=q=3/4$ in your case.)

For a discussion about the intuition behind this, see this question

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