Questions tagged [mixed-random-variable]

8 questions
8
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What is the distribution of $Z(X+Y)+XY$?

Given that $$ X \sim \mathcal{N}(0,1) \\ Y \sim \mathcal{N}(0,1) \\ Z \sim \mathcal{N}(\mu,1) $$ are independent, what is the PDF of $$ Z(X+Y)+XY $$ I tried to transform this expression to $$ \frac{1}{4}{\left( {X + Y + 2Z} \right)^2} - {Z^2} -…
5
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2 answers

does convolution of a probability distribution with itself converge to its mean

Suppose we have a probability distribution $f(x)$ with a finite support $[a,b]$. If we take the probability convolution of $\lambda f $ with $(1-\lambda)f,0 <\lambda<1$ recursively for many times, does the resulting distribution converges to the…
Emma
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2
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Mixed effect model with interaction

I am trying to explore the effects of an intervention on different outcome measures over time. In this example I evaluate the differences in the log-transformed data of my response variable (named: measurement) over time (time1 [baseline], time2,…
1
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1 answer

I'm lost in Crossover design-repeated measurements and mixed modelling

I am searching for days now, in what I think is a repeated measurements crossover design but I think I got mixed up reading up on it and I'm now going in circles so I was wondering if anyone could point me in the right direction. I was also…
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Proving the effect one fixed effect and the absence of effect of another fixed effect on a dataset (python and lme4)

Let's say I have data of a chemistry expriment: I have a sample of 11 probe coming from comparable material (ID01 to ID11, the random effect). I make process them with 2 different reactants (reactant A and Reactant B, 2 different fixed effect).…
ecjb
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Deconvolution of mixed signals from tumor data

I have N tumor-normal sample pairs from the same tissue of N subjects. For each sample, I have expression measurements for a fixed gene panel (M genes). The tumors are additionally also contaminated with normals. Therefore, the measurements in…
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How to determine appropriate numbres for m.lim in the dredge function in R?

I am working on a large dataset looking at effects of soil temperature, soil moisture and topography on greenhouse gases (GHG; CO2, CH4 and N2O). According to my hypotheses, I look at each GHG seperately with mixed models including random effects.…
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How can $X$ be a discrete random variable?

Suppose that the cumulative distribution function of discrete random variable $X$ is given by, $$F(x) = \begin{cases} 0 & \text{$x$ < 0 } \\[1.5ex] \dfrac{x}{4} & \text{$0 \leq x<1$}\\[1.5ex] \dfrac{1}{2}+\dfrac{x-1}{4} & \text{$1 \leq…