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Let $f(x)$ be the continuous probability density function of a random variable $x$, the probability that $a < x \leq b$, is :

1. $f(b-a)$
2. $f(b) - f(a)$
3. $\int\limits_a^b f(x) dx$
4. $\int\limits_a^b xf (x)dx$
asked | 2k views
+1

This might help ...

A) This is difference between probabilities don't know what it is !

B) This is cumulative distribution function . 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 continious random variable - >https://en.wikipedia.org/wiki/Expected_value

Ans => C
answered by Boss (42.4k points)
selected by
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(b) is not CDF
0
@Bikram sir How is b) part CDF
+3

(B) f(b)−f(a) is not CDF.

Reason: Here function f is pdf not cdf.

Note: If  X is Discrete RV  then P(a≤X≤b) = F(b) - F(a) ,where F is CDF .Both f and F are diffrent.

+1

@Akash Kanase and @Kapil I think selected answer requires small correction.

C should be used if prob density function is given B should be used if prob distribution function is given D must be used to calculate expectation when pdf is given
answered by Boss (14.1k points)