Mathematics Stack Exchange
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.

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Random Variables, Probability question

The question is: A type of algae is distributed in a liquid by the PPP (Poisson Point Process). We know that the number of algae is 2 per liter. Samples of these liquids are provided in containers with volume 20 cc. I'm trying to answer: Find the…
Thatdude1
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Probability of first player winning

Two players take turns to toss a coin; the winner is the first to toss a head. What is the probability that the first player to toss the coin wins?
Vaolter
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Difference of Independent Folded-Normal distributions

Let $Z \sim N(\mu,1)$, $X \sim N(0,1)$ and $Y \sim N(0,1)$ be independent random variables. By definition, the absolute value of a Normal random variable is said to have a folded Normal distribution. I'm trying to find: $\; P(|Z| >|Y|) \;$ and $…
Diana
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Conversion of Poisson distribution to Negative Exponential

A country bus driver picks up passengers randomly and independently at a mean rate of $\ 12$ per hour. The time at which he picks up his first passenger is $\ T$ hours. Explain why $$\ P(T < t) = 1 − e^{−12t} ~for~ t > 0.$$ Attempt Let's say the…
mathnoob123
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$Y_1, Y_2$ is a random sample of size $2$ from the uniform distribution...Find p.d.f of $U = Y_1+Y_2$

$Y_1, Y_2$ is a random sample of size $2$ from the uniform distribution on the interval $(0,1).$ Find the p.d.f. of $U = Y_1+Y_2$ I know the answer to the question, but don't understand how to get it. Particularly, I don't understand why the…
sucksatmath
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Finding the conditional mean and conditional variance

$$f_{X,Y}(x,y) = \begin{cases} \frac12 & \text{if |x|+|y| < 1} \\ 0 & \text{otherwise} \\ \end{cases}$$ Find the conditional mean and the conditional variance of Y given X=x. So far, I did: $$\begin{align} f_X(x) & = \int_{|x|-1}^{1-|x|} \frac12 dy…
woaini
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Continuity and differentiability of $ax+by$

Suppose $F$ is a cumulative distribution function of a random variable $X$ distributed in $[0,1]$ defined as follows: $$ F(x)= \begin{cases} ax+b & \text{if } x\leq a, \\ x^2-x+1 & \text{otherwise.} \end{cases}$$ where $a\in \left ( 0,1 \right )$…
onelessproblem
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Help on unclear question determining a probability distribution

The exercise of my homework assignment says "Let $E$, $F$, $G$ be independent events with probability $\frac{1}{2}$, $\frac{1}{4}$, $\frac{1}{5}$. Let $X$ be the number of events that occur. Determine the random variable $X$, its mean value and…
Eugenio
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Find the probability that the quadratic equation $x^2+Bx+C=0$ has real roots.

Let $B$ be the coefficient of $x$, and $C$ be the constant term in the quadratic equation:$x^2+Bx+C=0.$ Assume that $B$ is a uniform random variable on the interval $\left(1,3\right)$, $C$ is a uniform random variable on the interval…
jma
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Find the probability that the rectangle whose adjacent sides have lengths X and Y has area less than 8.

Let $X$ and $Y$ be the lengths in inches of adjacent sides of a rectangle. Assume that $X$ is a uniform random variable on the interval $(0,8)$, $Y$ is a uniform random variable on the interval $(0,4)$, and that $X$ and $Y$ are independent. Thus,…
jma
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What is the maximum entropy probability distribution on [0, 1] with a known mean?

I'm looking for a generalization of the Bernoulli distribution to the continuous domain of [0, 1]. The main requirement is that $E[x] = \theta$.
SherjilOzair
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How to determine distribution and expected value?

I am struggling with part ii) of the following question. How do I determine the distribution of $s$?
Callum Crosby
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What is the joint density for volume and surface area?

A machine produces cylindrical containers with the radii and the heights varying according to a joint pdf: \[ f_{R,H} = \begin{cases} 2r(r+2)h^{r+1}, & \text{if 0 < r, h < 1} \\ 0, & \text{otherwise} \\ \end{cases}\] What is the joint density for…
woaini
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What is the density of $Y = X^3$ if $X > 0$ and $Y = X^2$ of $X < 0$?

Let X be a continuous random variable with a density:\[ f_X(x) = \begin{cases} \frac 2{\pi}(1-x^2)^{1/2}, & \text{if |x| < 1} \\[2mm] 0, & \text{otherwise} \\ \end{cases}\] Find the density of:\[ Y = \begin{cases} X^3, & \text{if X > 0} \\ X^2,…
woaini
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100 coin flip bet

A client gave me this puzzle, which he claims I answered incorrectly. I'll give my answer and rationale, and his answer (for which he refuses to give a rationale). The Puzzle: You have a marker on a number line, it starts at zero. You also have a…
David M
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