Jointly distributed random variable

Definition:

• For any two random variables $X$ and $Y$, which will make up a new random variable of different distribution with distinct observations consists of both $X$ and $Y$
  • Unlike related variable, where observations of the same distribution is added
• For both discrete and continuous

Inequality between jointly random variable:

• $P(X_1<X_2)={\int }_{-\infty }^{\infty }{\int }_{-\infty }^{X^2}f(x_1,x_2)d{x}_{1}d{x}_2$
• $P(\frac{X_1}{X_2}<Z)\to P(Z<a)=P(\frac{X_1}{X_2}<a)=P(X_1<a{X}_2)={\int }_{X_2^l}^{\infty }{\int }_{X_1^l}^{a{X}_2}f(x_1,x_2)d{x}_{1}d{x}_2$

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