Linked Questions

0
votes
3answers
984 views

Intuition of pdf of a continuous random variable [duplicate]

What is the intuition behind the probability density function of a continuous random variable? Integrating it within two points provides the probability that is associated between two points, but if ...
0
votes
1answer
666 views

Solving for a pdf of a function of a continuous random variable. Justification and reason for the procedure [duplicate]

Short version: When solving for the pdf of a function of a continuous random variable(say, $Y=X^2$), why can't you just plug in inverse of that($\pm\sqrt{x}$) into the pdf of the RV? Why do you have ...
-1
votes
1answer
43 views

On transformations of random variables, discrete vs continuous [duplicate]

Suppose we have a discrete r.v. $X$, take $Y = g(X) $ where $g$ is one-to-one and onto- If we want to obtain the new pdf for the discrete r.v. we simply notice that $$f_Y(y) = P(Y=y) = f_X(g^{-1}(y)) ...
0
votes
0answers
59 views

Probability density function for a logarithmic spinner [duplicate]

I'm having trouble deriving the PDF for the following problem (from the book Doing Bayesian analysis with R and BUGS): Consider a spinner of the kind often found with board games, but with a ...
0
votes
0answers
25 views

Where can I find a citable reference for the formula for inverse distributions? [duplicate]

To be more specific: Let the random variable X be distributed according to probability density function f(x). Then the pdf of Y=1/X is given by g(y)=1/y^2 f(1/y), see wikipedia. I wonder if there is ...
15
votes
1answer
6k views

Derivation of change of variables of a probability density function?

In the book pattern recognition and machine learning (formula 1.27), it gives $$p_y(y)=p_x(x) \left | \frac{d x}{d y} \right |=p_x(g(y)) | g'(y) |$$ where $x=g(y)$, $p_x(x)$ is the pdf that ...
5
votes
2answers
4k views

Scale parameters — How do they work, why are they sometimes dropped?

I'm having difficulty wrapping my head around scale parameters. How exactly do they work? Why are they sometimes ignored? (in other words, when is it important to preserve them in a calculation?) ...
5
votes
2answers
3k views

Distribution of function of variable having a Gaussian distribution

If I have a variable $X$ whose Gaussian distribution is known and let $f$ be a known function, is there a way to compute the distribution of $f(X)$ i.e. the resulting Gaussian distribution from this? ...
5
votes
1answer
5k views

Cosine of a uniform random variable

I have to find pdf of $Y = \cos(X)$ where $X$ is a random variable distributed uniformly in $[-\pi,\pi]$. I solved this using distribution function method, and the result was: $f_{Y}(y) = \dfrac{1}{\...
3
votes
1answer
9k views

how to read y axis in kernel density graph [duplicate]

I need to understand how to read kernel density graphs. How do you come up with the values in y-axis?
10
votes
1answer
3k views

Different probability density transformations due to Jacobian factor

In Bishop's Pattern Recognition and Machine Learning I read the following, just after the probability density $p(x\in(a,b))=\int_a^bp(x)\textrm{d}x$ was introduced: Under a nonlinear change of ...
6
votes
2answers
3k views

Operations on probability distributions of continuous random variables

How do probability distributions of continuous random variables transform under functions? I.e. I have a random variable, X, drawn from a normal distribution with mean 0 and variance 1. What is the ...
2
votes
1answer
3k views

Base-10 lognormal PDF integrated over log10(x)

From what I understand, the lognormal probability density function in base-10 is mathematically defined thus: $$ p(x; \mu, \sigma) = \frac{log_{10}(e)}{x \sigma \sqrt{2 \pi}} e^{-\frac{(log_{10}(x) -...
3
votes
1answer
1k views

How to transform one PDF into another graphically?

To understand what I mean, let's use two well-known distributions: the normal and lognormal ones. From the dataset point of view, if you take normally-distributed data and take their exponential, you ...
3
votes
2answers
1k views

Why do the normal and log-normal density functions differ by a factor?

If a random variable $W$ is Normally distributed, then $\exp(W)$ is Log-Normally distributed. However, the pdfs of these two random variables differ by a factor of $\exp(W)^{-1}$. The Normal pdf ...

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