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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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discrete uniform distribution

if discrete random variable X is uniformly distributed over {-7,-5,-3,-1,1,3,5,7},then how to calculate the expectation of X and mod(X) and also expectation of X^2 and mod(X^2).It would be appreciable if it is diagramatically explained.
Ram Vanka
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Joint Probability of Four Coin Tosses

A fair coin is tossed 4 times. Let X be the number of heads in the first three tosses. Let Y be the number of heads in the last three tosses. Find the joint p.m.f. of X and Y . (Hint: There are only 2^4 = 16 equally likely outcomes when you toss 4…
Marko
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Z score confidence interval question

I have a question regarding how to answer this: Q: A credit risk study found that an individual with good credit score has an average debt of 15,000. If the debt of an individual with good credit score is normally distributed with standard deviation…
Hizumaru
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The effect of scaling arbitrary random varaible on its probability distribution?

Is it true that for an arbitrary random variable $X$, the distribution of $\frac{X}{2}$ is simply horizontally squeezing the original distribution to half of the original size and stretching it vertically to double of the original size? I mean…
Sam
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Would there be a well-known distribution for this problem?

I'm trying to think of a distribution to model the following situation. People enter a market having different beliefs. Two non-negative integers can represent the belief $G \in \{0,1,....\}$ and $B \in \{0,1,...\}$, the number of good and bad…
Anonymously lost student
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Does this violate the central limit theorem?

Recently I was trying to work out a random generator for a simulation. I wanted to generate multiple "scores", uniformly distributed over some range like 0 to 1, but I also wanted certain subgroups of these scores to be correlated with each other.…
user149485
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Distribution of max of ratio of a sequence of uniform variables

Consider a sequence of uniform random variables $X_i,i=1,2,\cdots,n$ in the interval $(0,1)$. It can be said that the density of ratio of two iid uniform variables in this interval is \begin{equation} f(z)= \begin{cases} \frac{1}{2},& 0
AgnostMystic
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Is there a joint distribution for binary and continuous variables?

As an example, let's imagine that we have the following four variables measured in 500 people: H - height in centimeters W - weight in kilograms B - whether the person is a member of a basketball team (binary variable) S - whether the person is a…
J. Doe
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Sum of random variables that are pareto-distributed

If we have $X_1, X_2, ..., X_k$ where all X's are pareto-distributed, what is the distribution of $X_1+...+X_k$? And what is the distribution of $a\cdot X_1$ if $X_1$ is pareto-distributed.
kasper kaspersen
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Mode of a Mixed Distribution

$X$ has the following mixed distribution: $P[0] = 0.2$ $$f(x) = \left\{ \begin{array}{cl} \frac{0.5xe^{\frac{-x}{100}}}{100} & x > 0 \\ 0 & \text{Otherwise} \\ \end{array} \right.$$ Calculate the mode of $X$ . I think the answer should be $0$ as…
Ankita Goyal
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PDF of Joint Distribution of $X$ and $Z$ given Joint Distribution of $X$ and $Y$ ; $Y$ and $Z$.

The Joint distribution of random variables $X$ and $Y$ has PDF $f(x, y) = x + y , 0 < x < 1, 0 < y < 1$. The Joint distribution of random variables $Y$ and $Z$ has PDF $g(y, z) = 3(y + 0.5 )z^2, 0 < y < 1, 0 < z < 1$ Which of the following could be…
Ankita Goyal
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The probability mass function given a new random variable

Say the random variable $Y = X^2 + 4$. And $P(X = -2) = 1/10, P(X = -1) = 2/5, P(X = 0) = 1/4, P(X = 1) = 1/5, P(X = 2) = 1/20$ How would you find P(Y = 8)? Additional question: Say W is the number shown on a biased six-sided die. We know…
Tingo Hugo
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Deriving the density function of a exponential distribution

I am reading a book where the author tries to derive the density function of a exponential variable by the following form: Suppose that in a short interval of time $\Delta t$ there is a chance $\lambda \Delta t$ that a event will occur. assuming…
Pedro Dreyer
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Probability distribution that an event (e.g. a meeting or a call) is in progress

I am considering events. They can be meetings, phone calls, etc. Let's say that a person is calling someone. Having both the probability distribution of event's start time and probability distribution of an event's duration, can the probability…
Oliver
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PDF of $\cos^2(\theta)$ where theta is uniformly distributed $[0, 2\pi]$?

I've seen examples where it's just $\cos(\theta)$ and the distribution is $$ \frac{1}{\pi \sqrt{1 - y^2}} $$ for $-1 < y < 1$ but I've never came across a squared cosine. I'm assuming we can use trig identities and go from there?
Khaled Q
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