# Questions tagged [joint-distribution]

Joint probability distribution of several random variables gives the probability that all of them simultaneously lie in a particular region.

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### Conditional expectation of two identical marginal normal random variables

Let $Y_0$ and $Y_1$ be both identically (not necessarily independent) normally distributed with mean $\mu$ and $\sigma^2$, i.e., $Y_i \sim N(\mu, \sigma^2)$ for $i = 1, 2$. Let $\rho$ denote the ...
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### Distribution given sum

I'm stuck on an exercise (it's not homework, but preparation for finals). It goes like this: $X_1, \dots, X_n$ are iid Exponential($\lambda$) (with parametrization $f(x)=\lambda e^{-\lambda x}$). What ...
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### Difference between the terms 'joint distribution' and 'multivariate distribution'?

I am writing about using a 'joint probability distribution' for an audience that would be more likely to understand 'multivariate distribution' so I am considering using the later. However, I do not ...
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### Estimating joint distributions using copula package in R

I am trying to estimate the joint distribution of stock returns using the copula package. I have read a couple of papers on copulae, but alas my lack of math ...
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### Necessary and sufficient condition on joint MGF for independence

Suppose I have a joint moment generating function $M_{X,Y}(s,t)$ for a joint distribution with CDF $F_{X,Y}(x,y)$. Is $M_{X,Y}(s,t)=M_{X,Y}(s,0)⋅M_{X,Y}(0,t)$ both a necessary and sufficient condition ...
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### Product of 2 Uniform random variables is greater than a constant with convolution

I am trying to formulate the following question. X and Y are IID , uniform r.v. with ~U(0,1) What is the probability of P( XY > 0.5) = ? 0.5 is a constant here and can be different. I do respect ...
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Suppose we have $X_{1} \sim B(m,p_{1}), X_{2} \sim B(m,p_{2}),\cdots, X_{n} \sim B(m,p_{n})$ and they are dependent. Does the joint distribution $f(X_{1},X_{2},\cdots,X_{n})$ have a closed form? Edit:...