# Tag Info

## New answers tagged probability

4 votes
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1 vote

### Can you have a "PMF-PDF" Together?

This is possible. It is standard measure theory and is done the same way as if all the random variables are continuous or all are discrete: You have a probability space $(\Omega, F, p)$ and your ...
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### Hazard function and survival analysis

If your plot is intended to be the probability density function for an event over time, $f(t)$ in the terminology of the answer from @Martin Georg Haas, then you technically have an improper ...
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1 vote

### How to interpret coefficients for a binary DV in an OLS model and constant value meaningfully?

There are a few different ways to model binary outcomes with an OLS approach, but the basic idea is that the coefficients represent the change in probability that the dependent variable is 1, holding ...
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### Hazard function and survival analysis

Answer Given that your $\lambda(t)$ actually represents the instantaneous probability to die at time $t$ (the hazard), your function $F(t)$ computes the probability to die before a certain time $t$. ...
1 vote
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### Joint distribution of longest run and number of runs in a sequence of $n$ coin tosses?

For the special case of $p=0.5$, the distribution is described by restricted integer compositions (see this post). $$F(n,k,w)=\sum_{j=0}^k(-1)^j\binom{k}{j}\binom{n-jw-1}{k-1}$$ where $n$ is the ...
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3 votes
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### Prove $P(X_1+X_2> 2C) \leq P(X_1>C)$ if $X_1,X_2$ are identical, but dependent?

Counterexample $$P(X_1 = 3, X_2 = 7) = P(X_1 = 7, X_2 = 3) = 0.5$$ Then $$P(X_1 \geq 4) = 0.5$$ and $$P(X_1 + X_2 \geq 8) = 1$$ Thus in this case $P(X_1 \geq c) < P(X_1 + X_2\geq c)$ Below is a ...
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### $X_i, X_j$ independent when $i≠j$, but $X_1, X_2, X_3$ dependent?

One that's perhaps easier to think about comes from a chessboard. Pick a point uniformly on the chessboard and consider $X_1$: row number (1-8) modulo 2 $X_2$: column number (1-8) modulo 2 $X_3$: ...
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### Distribution function of the linear combination of standardized student-t quantiles

Answers are in McNeil, Frey and Embrechts, "Quantitative Risk Management", Princeton 2005. Seems that, assuming a student-t multivariate distribution, linear combination of marginals is also ...
2 votes

### Statistical Models that "Exploit" Distributional Knowledge of the Predictor Variables

In regression models, by definition, we are interested in the conditional distribution of the response variable $Y$ given the observed predictors (covariates) $X$. Namely, if the joint distribution ...
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### Probability of outcomes from overlapping samples of a random variable

I'm not completely satisfied with this answer, but I think it's better than no answer. I'll attempt to answer the question posed in the comments: in a 100-by-100 matrix of independent Bernoulli trials ...
• 311
3 votes
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### What is the intuition behind the odds scale?

In the frequency interpretation, probability is the number of successful shots divided into the total number of shots (at each distance $x$). The odds is the number of successful shots per failure. ...
2 votes
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### probability that the players will exchange their initially drawn number

How about defining some cutoff value $q_1$ below which player 1 will decide to swap and a cut-off value $q_2$ below which player 2 will decide to swap. Then compute the win probability as a function ...
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### Notation of expectation with conditional in subscript

When you have a conditional expectation function, the input should be a function of the stipulated value of the conditioning variable. The conditional expectation is non-trivial only if the input ...
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0 votes
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### Fairness while counting chances

There is a reasonably well-developed physics/statistics literature on this topic There is actually a fairly well-developed literature on this matter in physics and statistics journals. Some good ...
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