# Tagged Questions

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### Laplace transform of noncentral chi-square distribution

I'm interested in non central chi-square distribution. More specifically, i want to derive the laplace transform of noncentral chi-sqruae disribution or density function. Let me know whether it ...
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### Generate quadrature points from a distribution

Is there any method to generate quadrature points from any arbitrary probability distribution, $p_{X}\left(x\right)$? We already know about Gauss Hermite rule for Normal distribution, Gauss-Laguerre ...
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Let $Z_{t}= W_{t}-tW_{1}$ and $Y_{1}=\sup_{0\leq t\leq 1}Z_{t}$, $(W_t, t \geq 0)$ standard Brownian motion Find the law of $Y_{1}$ I know that $\textbf{P}(\sup_{0\leq t\leq 1}W_{t}\geq x , ... 1answer 44 views ### Martingale based on normal PDF evaluated at normalized i.i.d. sums I have the following problem.$(X_n)_{n\geq0}, n\in\mathrm{R}$, is a family of iid r.v., normally distributed$\mathcal{N}(0,1)\mathcal{F_n} := \sigma((X_i)_{1\leq i\leq n})x\in\mathrm{R}, ...
Can someone provide an example of $X$ being a non-continuous random variable with continuous cumulative distribution function? For instance: $X$ is discrete if it takes (at most) a countable number ...