Questions tagged [mixed-random-variable]
8 questions
8
votes
1 answer
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} -…
Jiang Liu
- 81
- 4
5
votes
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
- 349
- 1
- 5
2
votes
2 answers
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
vote
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…
Tsitsi_Catto
- 13
- 2
0
votes
0 answers
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
- 539
- 1
- 5
- 16
0
votes
0 answers
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…
Stats_sc
- 1
- 1
0
votes
0 answers
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.…
Altariel
- 1
-1
votes
0 answers
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…
D ake
- 1