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Mathematics Stack Exchange

Questions tagged [probability-distributions]

Questions on using, finding, or otherwise relating to probability distributions, probability density functions (pdfs), cumulative distribution functions (cdfs), or other related functions. Use this tag along with the tags (probability), (probability-theory) or (statistics).

Any probability distribution, including beta, binomial, chi, Erlang, gamma, geometric, lognormal, negative binomial, normal (Gaussian), Pareto, Poisson, Student's t, uniform, Wald, Weibull, zeta, and Zipf.

28080 questions
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PDF of a piecewise transformation

This is a question that a friend asked me (has the final answer too). The pdf of a random variable $X$ is $$ f(x) = 0.5,\quad -1 < x < 1 $$ The random variable Y is defined as $$ Y = \begin{cases} -2X, & -1 < X < 0 \\ X+1, & 0 < X…
Ad22
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Can somebody provide an explanation of memoryless property in this example?

The following example is taken from the book "Introduction to Probability Models" of Sheldon M. Ross (Chapter 5, example 5.4). The dollar amount of damage involved in an automobile accident is an exponential random variable with mean 1000. Of…
hoangtuansu
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Find relating equation of M and N

P$X$(X)= Me^(-2|x|) + Ne^(-3|x|) is the probability density function for the real random variable X over the entire axis , M andN Both are positive real number . What will be the equation relating M and N? I considered it as a exponential function…
akash
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Value of cumulative distributed function at the origin

Consider a Gaussian distributed random variable with zero mean and standard deviation sigma. The value of its commulative distributed function at theorigin will be .... In this question, 4 options are There .out of which 0.5 is correct ans. Is…
akash
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An issue with the distribution function

I am reading a book about Boltzmann equation, here is a quotation: For a gas of $N$ particles, the number of particles having velocities in the $x$ direction between $c_x$ and $c_x + \mathrm dc_x$ is $Nf(c_x)\mathrm dc_x$. The function $f(c_x)$ is…
Syntax_ErrorX00
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Transformation technique to find PDF

Consider two random variables with the following joint PDF: $$ f_{X,Y}(x,y) = \begin{cases} 2, & x > 0, y > 0, x + y < 1 \\ 0, & \text{otherwise} \end{cases} $$ I need to find the PDF of $U = Y - X$. I'm having trouble determining the range of…
mmm
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Distribution of sum of weighted geometric random variables

Take $g_i$ to be a geometric random variable with parameter $1/2$, such that $$P(g_i = k) = \frac{1}{2^{k+1}}$$ for any integer $i$. I'm surprised at how much more difficult it is to evaluate this sum (of independent variables) $$\sigma \sim…
apg
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Simple question to check property of Normal Distributions.

So I was preparing for an entrance test and the study material provided by the institution has a lot of mistakes .Please forgive me if this seems off topic. I just know high school maths and I am studying Normal Distributions for the first time and…
Ishan Taneja
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Probability that X is greater than the mode of X?

How do I solve this problem: Let X be a continuous random variable with density function \begin{equation} f(x) = \begin{cases} \hfill ax^2e^{-10x} \hfill & \text{for x $\geq$ 0} \\ \hfill 0 \hfill & \text{otherwise} \\ …
Mestica
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Suppose that the continuous random variables X and Y ...

I've tried to attempt all these questions myself first but could someone tell me if these are correct?
NookLines
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Distribution of the sum of independent r.v.

Assume that $X_1$ and $X_2$ are independent random variables with given distribution $f(.)$ (say Normal distribution with $\mu_i$ and $\sigma_i$). I am stuck with the calculation of: $P(\{X_1 \leq a\} \; \cap\; \{X_2 \leq b\} \; \cap\; \{c \leq X_1…
Libra
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yet another problem about trinomial

An enterprise has workers divided in 3 groups. $p_i$ is a proportion of the $i$-th group to all, $p_1+p_2+p_3=1$. Select independently and equiprobably with replacement $n$ workers out of all, $X_i$ workers belong to $i$-th group. $n=X_1+X_2+X_3$.…
perry zhu
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a problem of trinomial distribution

$X_1$, $X_2$, $X_3$ are distributed according to the trinomial distribution with $n$($=X_1+X_2+X_3$) and $p_1$, $p_2$, $p_3$ ($p_1+p_2+p_3=1$). What is a correlation of $X_i$ and $X_j$? Is the conditional probability function $p(x_2,x_3|x_1)$ of…
perry zhu
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Computing mean of probability density function without integration

Is there any method of determining the mean of a random variable $X$ without integration?
user334784
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PMF of Bernoulli trials needed to produce at least one success and at least one failure

Let X be the number of Bernoulli(p) trials until we get at least one success and at least one failure. This means we need a string of successes followed by a failure or a string of failures followed by a success. $P(X = k) = p^{k-1}(1-p) +…
user137481
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