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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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Normal distribution with a probability less than 0.1?

The question states, "find the value of c where Z has a normal distribution with u=0 and variance=1 P(-2.7 < Z < c) = 0.0252 How do I find the c value for this problem?
Rap
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How is this a marginal distribution

I would like to understand the following sentence from Baxter and Rennie's book Financial Calculus: "There is a formal unity underlying the family - all the marginal distributions tend towards the same underlying normal structure" It refers to the…
Kristina
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What is the pdf of $X$ where its MGF is $1/(1+t)$?

$1/(1+t)$ $($ $ -1
Richard
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Grid probability problem

Let's say that you have a $5 \times 5$ grid. There is one correct square in each row. Your job is to make it across the grid. There is one correct answer in each row of the grid. You start by picking any of the five squares in the first row of the…
Matthew O'Connor
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Given $P(x)$ with a space what should $k$ be for $P(x)$ to be a p.d.f. of $X$?

The question is: If the probability of a random variable $X$ with space ${R_x} = \left\{ {1,2,...,12} \right\}$ is given by $P\left( x \right) = k\left( {2x - 1} \right)$, what should $k$ be for $P\left( x \right)$ to be a p.d.f. of $X$? I have the…
pabhp
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How would you plot f(x1) * g(x2) against x1*x2?

I have two graphs f(x) and g(x) which exist on the same infinite domain. I want to create a graph h(x) that plots f(x) * g(x) against x1 * x2 and I'm not sure how. To be precise, I want to take two univariate Gaussian distributions and graph them as…
Damyan Pavlovic
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How many light bulbs should be in stock

An institution has 5000 light bulbs put on the morning of everyday. One percent of them go out at the end of the day. Let $X$ denote the number of light bulbs that go out daily. How many light bulbs should be in stock, so that with probability 0.95…
Pedro Alvarès
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Sum of many Bernoulli random variable with different amplitude but same success probability

Let $Y = a_1X_1 + a_2X_2 + a_3X_3 +....a_nX_n$, where $a_i $ are just constants and $X_i$ are independent Bernoulli random variables with probability of 0.5. Then what would be the distribution of Y? Thanks!
Tianyu Wang
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Find the limiting distribution of the following trinomial distribution

Let $X_1,X_2,\dots$ be i.i.d. with the following probability density: $$P(X_j=0)=1-\frac{\lambda}{n}$$ $$P(X_j=1)=P(X_j=2)=\frac{\lambda}{2n}$$ Define $Y_n=\sum_1^nX_j$. Find $\lim_{n\rightarrow\infty} \psi_{Y_n}(t)$. I calculated the…
Shafat Arbaz Alam
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Uniform PDF of offset sphere

Note that throughout this I use the spherical mapping convention: $$(x,y,z) = (r\cos\phi\sin\theta,r\cos\theta,r\sin\phi\sin\theta)$$ I have derived that the uniform pdf for a sphere $S_1$ with radius $\rho$ and center $(0,0,0)$ is…
lightxbulb
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Calculating the probability of a vector of standard normal distributed variables.

Let $X,Y$ be two i.i.d random variables with standard normal distribution which is the probability that the vector $(X,Y)$ to be in the second quadrant with distance to the origin greater than $2$? What I think I am being asked is to calculate…
John Keeper
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relation between moments of discrete random variable and CDF

Consider a discrete positive random variable, say X. This link nicely shows that \begin{equation} E[X] = \sum_{k=0}^{\infty} (1-F(k)) \end{equation} Moreover, \begin{equation} E[X^2] = \sum_{k=0}^{\infty} (2k+1)(1-F(k)) \end{equation} I am puzzled…
Alexander K.
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Indicator function of an exponentially distributed random variable.

If $X\sim\mathrm{Exp}(1)$ how do I have to interprete: $$ Y = \textbf{1}_{[c,\infty)}(X) $$ where $\textbf{1}$ is the indicator function. I realize that $Y$ is $0$ if $X < c$ and $1$ if $X >= c$. But how do I calculate the probability distribution…
RedCrayon
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What is the frequency distribution of a random variable representing the result of the launch of one dice?

What is the frequency distribution of a random variable representing the result of the launch of one die? I don't if that is correct but: $S = \{1,2,3,4,5,6\}$ The probability of $\{1,2,3,4,5,6\}$ is the same, $\frac{1}{6}$. Can I say: $X$ ~…
richardaum
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Finding Density Function of Transformation

Let $Y$ be uniformly distributed over the interval $(−1, 3)$. Find the probability density function of $U = Y^2$. Attempted solution: We know that $$ Y=\begin{cases} 1/4 && -1 \leq y \leq 3\\ 0 && \text{elsewhere} \end{cases} $$ We find the CDF…
Bryden C
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