# Questions tagged [pdf]

Probability density function (PDF) of a continuous random variable gives the relative probability for each of its possible values. Use this tag for discrete probability mass functions (PMFs) too.

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### Is it possible for a distribution to have a non-zero probability of generating a value with zero probability density?

I am reading the book "An Elementary Introduction to Statistical Learning Theory" and there is a sketch of a proof (Section 8.4) for the universal consistency of kernel rules for binary ...
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### How to estimate parameters and pdf of a random variable transformed from a lognormal random variable?

I have a continuous random variable Y that follows lognormal distribution with known parameters (mu and sigma). Let Y be transformed to X=Y-20000. So it is basically shifted to left. How do I find the ...
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### Finding PMF, CDF of a piecewise function of an RV

Here's the question: Let $Z$ have CDF $F$ and pdf $f$ and let $A$ be a subset of the real line. Further, let \begin{cases} W = 1 & \text{if $Z \in A$} \\ ...
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### Why are there two ways to write PDF and CDF functions?

I often see PDF and CDF functions written as either $f_X(x)$ or $f(x)$ for PDF or $F_X(x)$ or $F(x)$ for CDF. In what situations would you use either notation? Like what is the point of having ...
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### What is the reason that a likelihood function is not a pdf?

What is the reason that a likelihood function is not a pdf (probability density function)?
I have a state machine with positive and negative inputs. The time between positive inputs follows a gamma distribution ($X_+ \sim \Gamma(k_+, \theta_+)$), and the time between negative inputs follows ...
In survival analysis, one may arrive at a series of samples $X_1,...,X_n$, for which the outcome of a given $X$ may not be "observed" within the experiment. For instance, if the $X_i$'s are failure ...