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I understand probability distribution but I am having a hard time getting a grasp on probability density function, specifically difference between dexp (density of exponential distribution) and pexp (probability distribution of exponential distribution)

bison2178
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  • It's not clear what you mean. What do you intend by "probability distribution"? Are you referring to the [cdf](http://en.wikipedia.org/wiki/Cumulative_distribution_function), or something else? – Glen_b Aug 15 '14 at 05:07
  • Glen, are cdf and simply density function both the same ? – bison2178 Aug 15 '14 at 05:15
  • No, they're different. The density is the derivative of the cdf, the cdf is the integral of the density. The cdf is $P(X\leq x)$. – Glen_b Aug 15 '14 at 05:56
  • Thanks Glen I think I am little more closer to my understanding now, I used this example for exponential distribution where λ=4 and x=0.5 in the case of pdf exp(λ=4,x=0.5) is 0.89 for density function exp(λ=4,x=0.5) is 0.54.... – bison2178 Aug 15 '14 at 07:15
  • wait, no, you're confused -- "*pdf*" is exactly the same thing as "density function" – Glen_b Aug 15 '14 at 07:45
  • Okay lets go back to the example i mentioned earlier exponential distribution exp(λ=4,x=0.5) how will you frame a question addressing a density function, how will you frame a question addressing a distribution function ? – bison2178 Aug 15 '14 at 23:13
  • I don't understand what you're asking there. If I am framing a question asking about the density, I'll ask about "the density", or "the pdf". If I am asking a question about the distribution function, I'll ask about "the distribution function" or "the cdf", so I'd frame a question in those terms. Could you clarify what you're after? – Glen_b Aug 16 '14 at 00:11

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Suppose X is an exponential random variable. pexp(c) is the probability that X is less than or equal to c. pexp is always non-decreasing. To prove this, let m>0, then pexp(c+m)=P(X

dexp(c) is the derivative of pexp(c), but intuitively, it is the probability that X is 'near' c, or the 'density' of the probability mass. The chance X lands on exactly each number is zero, but when we sum over the infinite real numbers in any interval, we get a finite probability that X falls in that interval. This is decreasing, since an exponential random variable is more likely to be between 1 and 2 than between 100 and 101.

A CDF is NOT a density function. A density is a mass divided by a length. A CDF doesn't define the length where the probability mass is, just that it is left of c.

user7868
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    Let me start from here, density is the derivative of distribution and CDF is the integral of the distribution is that correct ? – bison2178 Aug 15 '14 at 06:08