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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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Difference in pdf formula between Dirichlet and Multinomial distributions

The pdf for Dirichlet distribution seems to be $$ Dir(\alpha_1,\alpha_2,\ldots\alpha_k) \text{ is defined as} $$ $$ pdf(θ_1,θ_2,\ldots,θ_k )= \frac{Γ(\alpha_0)}{Γ(∝_1 )Γ(∝_2 )\cdots Γ(∝_k )} θ_1^{∝_1-1} θ_2^{∝_2-1} \cdots θ_k^{∝_k-1} $$ $$ \text{…
Ranjan
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Generating an asymetric triangular distribution

I am trying to generate an asymetric triangular distribution; a is lower limit, b is higher limit and c is mode. I found this following way to generate a random variable $X$ with triangular distribution. Let $β = (c-a)/(b-a)$ Let $U_1$ and…
marvinthemartian
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Difference between Gaussian distribution and Laplace distribution?

there. I always appreciate the members belong this site because very active support! Now I have some data set which were measured by same experimental setup, but their distributions were slightly different I think. Distribution of some look like…
actlee
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Different ways of calculating the conditional probability in the continuous case

For simplicity, assume a joint pdf of 2 variables $f(x,y)$. Say we have two events $A$ and $B$. How would one calculate: $$\Pr[A \mid B]$$ if we have continuous pdfs in question? I would have thought that one way to do it is as follows: $$ \Pr[A…
Charlie Parker
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Let X and Y be geometrically distributed iid r.v.s. Find the pmf of min(X, Y), and the pmf and Z = X - Y.

Let X and Y be geometrically distributed iid r.v.s. Find the pmf of M = min(X, Y), and the pmf and D = X - Y. I thought $$ P(M = m) = P(X = x) \cdot P(Y > x) + P(Y = y) \cdot P(X > y) + P(D = 0)$$ $$ = 2 \cdot P(X = x) \cdot P(Y > x) + P(D =…
Pie_day_1239191919
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How do I prove that this discrete distribution satisfies Chebyshev’s inequality?

I have been given a discrete distribution, which has variance $\sigma^2$ and mean $\mu$. There are three $X$ values in terms of $k$, $\mu$ and $\sigma$, while the probabilities are in those terms too. I need to find out how this distribution…
Tom
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Find Joint Distribution (marginal is known)

Got stuck...need help on the following question Given: $Y \sim f_Y(y)=\frac{1}{\theta }e^{-\frac{y}{\theta }}$, $y>0$. $R\sim g(r)$, $r>0$ $Y$ and $R$ are independent random variables. $Z=YR$ Q: Find the joint density of $(Z,R)$ It is quite weird…
Liz Sugar
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$f(x,y) = \alpha^2 e^{-\alpha y}$, $0 \leq x \leq y \leq 1$. Find the Joint Distribution of X and Y.

Full Disclosure: I am a graduate student taking a class in probability. I am working through extra problems in the Hoel, Port and Stone book which has answers in the back of the textbook. I am not doing these problems for homework, merely as a…
Clan_Destine
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Probability normal distribution P(X>Y)?

Angelo earns every month as a variable normal X N(1000;400^2), Bruno N(1400;300^2). Calculate the probability of Angelo earns more then Bruno p(X>y)?
James
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A question of Joint PDF

I have not idea about part a. I know I need to prove the integration of f(x,y)=1, but how should I deal with the range of x and y.
kenxilo
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Expected Values probalem

The problem is: In a world without gravity, a very small gun shooting point-like balls is located at the lower left end $(0, 0)$ of a $2D$ corridor. The corridor has length $L = 100\thinspace m$ and height $h = 5\thinspace m$. The gun shoots with…
phil
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If $f(x)$ belong to set of probability distributions, then what can be deduced about $\frac{1}{a} f(\frac{1}{a}\cdot x)$

My question is in the context of probability distributions, whose Fourier transforms (characteristic function) almost always exit. If $f(x)$ be some function such that $ \int_{-\infty}^\infty f(x) \, dx=1,$ then what can be said/deduce about $…
kaka
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calculating exponential distributions for products going bad

half of our products (follows an exponential distribution) gone bad during a a week. calculate how long does it take for 1/3 of the products to go bad? my answer (I put this in calculator and get no results): the correct answer is suppose to be 1.6…
user2864059
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joint probability distributions

The problem is: I have two partially overlapping histograms of different shapes, each corresponding ultimately to a certain fraction, let's say one histogram represents the value 50% and the other 40%. Then I have point and its uncertainty located…
maya
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Bus Problem: Binomial Distribution

For every 10,000 miles driven, the probability that a school bus in the United States will be in at least one accident is 1/6. For 12 buses in the lot, what are the probabilities that: assume that each is driven 10,000 miles. So I think that I have…
Math Major
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