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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 in Probability by Veteran (18k points) | 1.6k views

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2 Answers

+11 votes
Best answer
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 Veteran (49.5k points)
selected by
(b) is not CDF
@Bikram sir How is b) part CDF

 

(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.

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

+13 votes
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 Veteran (14.3k points)


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