# Questions tagged [bivariate]

Joint probability distribution of two variables.

234 questions
Filter by
Sorted by
Tagged with
7 views

### What is an example of a bivariate distribution that is dependent but nonlinear dependence?

I've seen plots of bivariate normal where the two variables are correlated. This results in a elongated peak area. What would a bivariate distribution look like if the two are dependent on each other ...
20 views

### Relation between bivariate survial function and cumulative density function

I am trying to understand why $Pr(T_1> t_1,T_2 > 2)=1-F_1(t_1)-F_2(t_2)+F_{12}(t_1,t_2)$ My derivation is as follows: \begin{align} Pr(T_1> t_1,T_2 > t_2) &=Pr(T_1> t_1\mid T_2>...
23 views

### bivariate normal distribution meaning [duplicate]

Does bivariate normal distribution mean the two random variables have normal distributions? is that enough for two random variables to have a bivariate normal distribution or are there some other ...
22 views

39 views

34 views

### Expected distance between (X, Y), where both X and Y are standrd normal random variabls and the origin

Let $(X, Y)$ be two independent standard random variable, with mean and SD being 0 and 1 respectively. What would be $E[\sqrt(X^2 + Y^2)]$, the expected distance between $(X, Y)$ and the origin.
98 views

### Bivariate exponential distribution $(S, T)$ with controllable correlation and $S\leq T$

I am trying to define a bivariate exponential distribution $(S, T)$ with marginals $S\sim\mathrm{Exp}(\lambda_S)$ and $T\sim\mathrm{Exp}(\lambda_T)$ for $\lambda_S > \lambda_T$. I would like the ...
120 views

### How can I find $\rho$, given $P(4 < Y < 16|X=5)=0.9544$?

Let $X$ and $Y$ have a bivariate normal distribution with $\mu_X=5, \mu_Y=10, \sigma^2_X=1, \sigma^2_Y=25, \rho >0$. If $P(4 < Y < 16|X=5)=0.9544$, I would like to find $\rho$. I know that ...
133 views

### How do I show that $Y=2\sqrt{X_1X_2}\sim$Gamma$(2p,1)$?

Suppose that $X_1\sim$Gamma$(p,1)$ and independently, $X_2\sim$Gamma$(p+1/2,1)$. Show that $Y=2\sqrt{X_1X_2}\sim$Gamma$(2p,1)$. This problem followed a section on bivariate transformations, so I ...
### Example: Writing the joint PDF $f(x, y)$ as the product of a marginal and a conditional probability function
I am presented with the following notes on Bivariate distribtions: If we can write the joint probability density function $f(x, y)$ of a pair of random variables $(X, Y)$ as the product of a ...