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Probability density function (PDF) of a continuous random variable gives the relative probability for each of its possible values. Use this tag for discrete probability mass functions (PMFs) too.

2
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$P( Y \leq y) $ $= P( Y \leq y|X=1)P(X=1) + P( Y \leq y|X=0)P(X=0)$ $=P( Y \leq y|X=1)p + P( Y \leq y|X=0)(1-p)$ $=pP( W\leq y) + (1-p)P( Z \leq y)$ So $F_Y(y)=pF_W(y)+(1-p)F_Z(y)$ and thus $f_Y(y …
answered Oct 27 '13 by Henry
9
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An equivalent result is well known in survival analysis: the expected lifetime is $$\int_{t=0}^\infty S(t) \; dt$$ where the survival function is $S(t) = \Pr(T \gt t)$ measured from birth at $t=0$. ( …
answered Nov 15 '11 by Henry
11
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From the R package MASS, of the $506$ total observations in Boston, $369$ have a value for tax below 470 and $137$ have a value for tax above 665. In fact 666 is by far the most common value in the d …
answered Feb 12 '14 by Henry
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You can extend your non-parametric method if your original sample is large enough. Suppose you wanted to have a 95% probability of not rejecting the null hypothesis that your new observation comes …
answered Sep 17 '13 by Henry
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You should not have $X_1$ in the marginal distribution for $X_2$ I would expect you to get $P(X_2 \le x_2) = x_2 (1-\log(x_2))$ and so the derivative gives a marginal density of $-\log(x_2)$. This …
answered Feb 25 '11 by Henry
2
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Here is one made specially for you. Note that the density of a distribution symmetric about $0$ is the same for positive and negative values. density cumprob -3.5 0.0008726827 0.00023 …
answered Dec 17 '12 by Henry
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I would call $f_t$ the instantaneous rate of the process at time $t$, or perhaps the hazard function So, for example, you can find the expected number of arrivals between time $a$ and time $b$, whi …
answered Oct 17 '18 by Henry
5
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A simple example would be if you bought a light-bulb with a lifetime which was exponentially distributed with a mean of 1000 days. With a 95% credible region: would you tend to see it as likely to l …
answered Mar 14 '12 by Henry
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In your link, you have the cumulative distribution function for the logistic distribution as $$\frac{1}{1+e^{-\frac{x-\mu}{s}}}$$ while in your question you have $$\dfrac{\exp(w^TX)}{(1+\exp(w^TX))} …
answered Oct 1 by Henry