A probability provides a quantitative description of the likely occurrence of a particular event.

learn more… | top users | synonyms (3)

0
votes
1answer
23 views

$H_0=250g$ and $H_1\neq 250g$"

We have a sample of size $100$ with a standard deviation of $5g$ It was decided that if the sample mean is between $245g$ and $255g$ while the sample average is $250g$ if $\mu=250g$ or $\mu\neq250g$ ...
0
votes
1answer
32 views

Coupon collecting problem

Suppose there are 8 different types of coupons, each coupon has probability 1/8 of being selected. Suppose a total of 6 coupons are collected. Let: $$ X_i=\begin{cases} 1, \textrm{if a type-i coupon ...
1
vote
0answers
12 views

A Hypothesis Testing Question and Verification

Suppose we have two p.d.f.'s: $f_0(x)=1,$ if $0\leq x\leq1$, and $f_0(x)=0$ otherwise $f_1 (x)=2x$ if $0\leq x\leq1$, and $f_1(x)=0$ otherwise We want to test the hypotheses ...
2
votes
1answer
17 views

Developing a heuristic for maximizing the “covering” of a distribution

Context There's a board-game called Settlers of Catan in which players compete to be the first to gain 10 victory points by trading various resources in exchange for pieces (or cards) worth victory ...
0
votes
1answer
20 views

How to estimate rating of a customer?

I have data about customers transactions contains: ratings of customer $r_{ci}$ to service $s_m$ which has quality $q_m$. Quality is assumed to be a real value from [0, 1]. Rating is discrete values ...
0
votes
1answer
21 views

Does martingale model work for betting football matches?

Imagine I have 1 million USD and will be betting 1.000 USD on the win of FC Barcelona each time they play a match in La Liga (Spanish Tier 1 football league). If FC Barcelona loses or ties their last ...
1
vote
1answer
20 views

how to random sample proportional to probabilities

I have a ten-sided die, where I know the probabilities of rolling some, but not all of the values on the die: ...
1
vote
0answers
28 views

how to determine if two dice are fair using pymc and roll data

My scenario is that I have two six-sided dice (D1 and D2), either of which may be fair or loaded (biased). I have samples of combined roll data (i.e. D1 + D2). I would like to view the posterior ...
2
votes
1answer
34 views

What is the distribution family where one side is with light tail but the other side with heavy tail?

For example the distribution of weights of human. There are not many adults under 40 kg, but a lot more people heavier than 100 kg, although the average of an adult's weight is, let's say, 70 kg. ...
0
votes
0answers
24 views

Probability distrubution of 3 products

A lightbulb factory produces bulbs in 3 qualities. 50% of production is Low quality, 30% average quality, 20% good quality. A randomly selected lot of 4 bulbs gets tested. Low quality lights have a ...
3
votes
1answer
20 views

Variance of a linear combination of vectors

Let $A$ and $B$ be two constant matrices and let $x$ and$ y$ be two random vectors, what is the general formula for $Var(Ax+By)$? I know the formula for when $x$ and $y$ are scalar random variables ...
1
vote
0answers
12 views

Describing a distribution of probabilities/percentages

Is there a better way to describe this probability? \begin{equation} Pr(Y_{sij}|R_n) = \frac{Y_{sij|R_n} \sum_{ij}Y_{sij}}{\sum_{ij|R_n} Y_{ij}\sum_{sij}Y_{sij}} \end{equation} The $R_n$ describes ...
0
votes
1answer
23 views

What is a good model for revenue managment / price optimization problem

I am trying to create a dynamic pricing model to optimize revenue for a hypothetical business. Lets say I have an application that connects dog walkers to people who want to pay for their dog to get ...
3
votes
0answers
25 views

Regarding variance of “total number of records”

Here is my problem: Let $\{X_i\}_{i=1}^n$ be a sequence of continuous random variables. A record is said to have occured at time $k$ if $X_k > X_i$ $\forall i=1,...,k-1$. Let $N$ denote the ...
0
votes
0answers
30 views

What are the odds of this happening?

There is a list of exactly 94 names on it. One person randomly picks 5 names on the list and doesn't show them to anyone. Another person picks just 2 names on the list. What are the odds that one of ...
1
vote
0answers
16 views

Probability of paired combinations

There are 8 friends: Alfred, Alex, Billy, Barbara, Connie, Chris, David and Donna. The friends are paired up at random. What is the probability that at least two pairs will share the same first ...
0
votes
0answers
26 views

Threshold for Pearson correlation for hypothesis testing [on hold]

How to determine threshold for Pearson correlation coefficient which reduces type 1 and 2 error and and can be used whether the sample is correlated or not?
0
votes
0answers
40 views

statistical analysis problems [on hold]

Two persons, A and B, are to play a series of independent games, with A’s winning probability in each game = $p$ and B’s winning probability = $q = 1 – p$. The game ends when the total number of ...
1
vote
0answers
29 views

Estimate Probability of being in a time interval

​You arrive at a bus stop in an unfamiliar part of town. Assume that buses arrive at the stop with an unknown (to you) distribution and wait in the bus stop for a few ​minutes. The wait time ...
5
votes
3answers
375 views

Returning unlikely results from a probability distribution

The Law of large numbers addresses the issue of the average result of a large number of random trials. Is there a similar law which addresses the probability of obtaining an unusual result for a large ...
1
vote
0answers
29 views

Confidence intervals sum of dependent variables

How to construct confidence intervals for sum of dependent random variables. Specifically, I want a high probability claim regarding the difference between the empirical mean and the true mean of the ...
0
votes
0answers
4 views

Find the probability of a new data point using “density” function in R [migrated]

I am trying to find the best PDF of a data that has Gaussian distribution, using the "density" function in R. Now, given a new data point, I want to find the probability of this data point based on ...
31
votes
6answers
3k views

How to tell the probability of failure if there were no failures?

I was wondering if there is a way to tell the probability of something failing (a product) if we have 100,000 products in the field for 1 year and with no failures? What is the probability that one of ...
1
vote
0answers
27 views

Calculate the probability of a string

I have a classification problem. I am trying to classify strings using I normalize the data before training. So far I get the best results with addition, but I cannot understand why. The ...
2
votes
0answers
41 views

Bayesian credible intervals: “superiority” even if 1 is included?

In a recent medical publication comparing a cardiac device to anticoagulation ("blood thinners") using a Bayesian statistical model to evaluate the efficacy of preventing strokes and cardiovascular ...
0
votes
0answers
17 views

rate of convergence of sample mean

Law of large number ensures the convergence of sample mean to population mean. But it does not tell about the rate of convergence. Now CLT tells about the rate of convergence. Then what is the ...
-1
votes
0answers
13 views

survival mixture model of gamma distribution via EM algorithm

I generated survival data for a three component survival mixture of gamma distribution with random right censored observations in R with the code; ...
3
votes
2answers
187 views

Independence and orthogonality

I know what it means to say two variables are independent, but can't understand what does it mean to say two variables are orthogonal.Can anyone help me?
1
vote
1answer
37 views

Why $p(y_n|y_{0:n-1})$ is a constant in Kalman filter derivation?

In a derivation of Kalman filter, It says that in Equation: $p(x_n|y_{0:n})=\frac{p(y_n|x_n)p(x_b|y_{0:n-1})}{p(y_n|y_{0:n-1})}$ the denominator $p(y_n|y_{0:n-1})$ is a constant. (See the ...
0
votes
0answers
7 views

Dempster-Shafer sampling

If we consider classical probability on finite support, we assign some probability to each elementary event. The sampling is then easy. In Dempster-Shafer, we assign a value to all subsets of the ...
0
votes
1answer
34 views

Is summing posterior probabilities valid for classification problems?

A classification for two mutually exclusive problem can be formulated by having a decision hinge on whether $P_0(x) > P_1(x)$ or $P_0(x) < P_1(x)$ where $P_0(x)$ and $P_1(x)$ are posterior ...
1
vote
0answers
17 views

Laplace transform of function of more than one random variable

I have tried to be very clear and precise with this question. Please let me know if I can write it in better way or give more explanations. I don't need a solution for this problem, only opinion if my ...
1
vote
1answer
32 views

How to calculate probability that another player has a card

In a poker game, how would we calculate the probability that another player has at least one certain card? Lets say that there are five other player, there are four cards in middle of the table, and ...
0
votes
1answer
44 views

Graphical dependence in the DAG X->Z<-Y

In Barber's book pp. 40-41 he says that the belief network X->Z<-Y: is "graphically dependent" since: $$p(x,y|z) \propto p(z|x,y)p(x)p(y)$$ I don't understand why graphical dependence follows ...
0
votes
0answers
28 views

How is the probability of Weibull Distribution exceed $1$ for some value? [duplicate]

Here is R code which show that probability of Weibull distribution is $1.7$ for some value $t$. But as far i know probability lies between $0$ and $1$. How is it possible ? R code: ...
2
votes
0answers
78 views

Birthday paradox, two generations, different continents

I have been reading about the birthday paradox & was trying to take it further & apply it to an example from my own life:- I am a Brit married to an American. My British sister-in-law shares ...
3
votes
0answers
28 views

If X is independent of Y given Z, is X/Z independent of Y?

When is the following true? If $X$ is independent of $Y$ given $Z$, $\frac{X}{Z}$ is independent of Y.
1
vote
1answer
35 views

Variation on the urn problem and frequency distribution

I have $6$ machines each producing different coloured balls. The balls are mixed together in a large vessel. Groups of $6$ balls are extracted at random for packing. Each pack will therefore have a ...
2
votes
0answers
29 views

parameter and prediction confidence intervals

We have a correctly specified linear model $z = x\beta + \varepsilon$ with 100 independent observations. Given: $y = e^z$, $\sigma^2 = 4$ (assumed to be known), sample means $\bar{x} = -3$ and ...
0
votes
1answer
45 views

Can E[X|Y] be computed from E[X|Y,Z]?

Let X, Y and Z be 3 discrete random variables. Is the following true? $\sum_{i=1}^\infty P\{Y=i\} E[X|Y=i,Z] = E[X|Z]$
3
votes
1answer
46 views

Conditional probability of an event given two independent events

I am dealing with an interesting probability problem. I had $16$ subjects randomly divided into $4$ different rooms, each room having $4$ seats. The subjects were given a question to solve. We knew ...
4
votes
1answer
105 views

What does a very high odds ratio in binary logistic regression indicate?

I am developing a predictive model to apply to raster layers for land cover classification. So, I have a thematic category that is classified as agriculture but an accuracy assessment indicates ...
0
votes
0answers
35 views

comparing probability histogram

I have two probability histogram samples. I know there are methods(i.e KS test etc) out there to compare histograms but I am trying to compare through simple sum of absolute difference between these ...
1
vote
1answer
35 views

Is it possible to compare probabilities of 2 logistic different models?

Is it possible to compare probabilities of 2 logistic different models? For example if I have one model that returns the probability that someone answer a phone call on Mondays, and then I have ...
2
votes
1answer
104 views

How to simulate a system where “the failure probability per week is 3.5%”?

I have system described by a statement like "The failure probability per week at 20 Celsius degree is 3.5%", how can I simulate such a system? The simulation I have in mind should answer to questions ...
-1
votes
1answer
31 views

Problem of summation of conditional probabilities [closed]

Let $A$ be event in a stochastic space, $A=\cup_i \{a_i\} $, and $P(a_i|A)$ and $P(A|a_i)$ the corresponding conditional probabilities. What is the sum, over all $i$, of the $P(a_i|A) / P(A|a_i)$ ...
3
votes
0answers
57 views

Draw balls from two different binomial distributions. What $r^2$ do you expect to find?

We have $N$ buckets in which we will put some balls. Before that, the buckets are split into two groups, group $A$ and group $B$. The number of balls that we will put in each bucket is drawn from a ...
7
votes
3answers
65 views

Proof that the probability of one RV being larger than $n-1$ others is $\frac{1}{n}$

This is a follow-on from my previous question about samples from a distribution. Suppose $X_1 \ldots X_{n-1}, X_n$ are random variables all following some fixed distribution $D$. How do I prove that ...
0
votes
0answers
15 views

Expected value of multiple events

There are three offers Offer A - $ 5 probability of redemption A - P (A) = 0.5 Offer B - $ 4 Probability of redemption B – P(B) = 0.6 Offer C - $ 3 probability of redemption C – P(C) = 0.7 If I ...
0
votes
1answer
24 views

Basic probability with dice

This is probably (...) a very basic probability question, but I'd like to be sure about it. I have 6-sided dice. When rolled, I count one success per dice if the number on the dice is 5 or more. for ...