Joint distribution

Joint distribution in probability theory is the distribution of joint outcomes. $(\xi _{1},\xi _{2},\ldots )$ ${\ displaystyle (\ xi _ {1}, \ xi _ {2}, \ ldots)}$ ${\ displaystyle (\ xi _ {1}, \ xi _ {2}, \ ldots)}$ formed from several random variables $\xi _{1},\xi _{2},\ldots$ ${\ displaystyle \ xi _ {1}, \ xi _ {2}, \ ldots}$ ${\ displaystyle \ xi _ {1}, \ xi _ {2}, \ ldots}$ . For example, if a random variable $\xi _{1}$ ${\ displaystyle \ xi _ {1}}$ $\ xi_1$ is the result of throwing the first die, and the random variable $\xi _{2}$ ${\ displaystyle \ xi _ {2}}$ $\ xi_2$ is the result of throwing another dice, the result $(\xi _{1},\xi _{2})$ ${\ displaystyle (\ xi _ {1}, \ xi _ {2})}$ ${\ displaystyle (\ xi _ {1}, \ xi _ {2})}$ joint throwing of dice is a composite random variable and has a joint distribution.

Definitions

If a $\xi _{1},\ldots ,\xi _{n}$ ${\ displaystyle \ xi _ {1}, \ ldots, \ xi _ {n}}$ - random variables, then each compound value ( $\xi _{1},\ldots ,\xi _{n}$ ${\ displaystyle \ xi _ {1}, \ ldots, \ xi _ {n}}$ ) is also a random variable. Its distribution is called the joint distribution of random variables. $\xi _{1},\ldots ,\xi _{n}$ ${\ displaystyle \ xi _ {1}, \ ldots, \ xi _ {n}}$ . ^[1] .

Links

↑ Harald Kramer, Mathematical Methods of Statistics, translated from English by A. S. Monin and A. A. Petrov, edited by Academician Kolmogorov, second edition, stereotypical, chapter 14.2, page 177., http://ikfia.ysn.ru/ images / doc / Teoriya_veroyatnosti_i_mat_statistika / Kramer1975en.pdf Archive copy of February 6, 2018 on the Wayback Machine

[1] Harald Kramer, Mathematical Methods of Statistics, translated from English by A. S. Monin and A. A. Petrov, edited by Academician Kolmogorov, second edition, stereotypical, chapter 14.2, page 177., http://ikfia.ysn.ru/ images / doc / Teoriya_veroyatnosti_i_mat_statistika / Kramer1975en.pdf Archive copy of February 6, 2018 on the Wayback Machine

Joint distribution

Definitions

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