$P(x=a)=\int_a^af(x)dx=0$

Probability at discrete point=0

So here random variables should be defined as continuous not discrete

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gatecse
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in Probability
Sep 21, 2014

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Best answer

$A.$ This gives the probability at the point of $b-a$ which is not having any significant w.r.t $a$ and $b.$

$B.$ This gives the difference of the probabilities at $b$ and $a$. Note: This is different from cumulative distribution function $F(b) - F(a).$ Ref: https://en.wikipedia.org/wiki/Cumulative_distribution_function

$C.$ This is Probability Density Function. Ref: https://en.wikipedia.org/wiki/Probability_density_function

$D.$ This is expected value of continuous random variable. Ref: https://en.wikipedia.org/wiki/Expected_value

Answer is $C$.

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