Let $(X,Y)$ be random vector and ${\varphi _{XY}}({t_1},{t_2}) = {\rm{E}}{e^{i({t_1}X + {t_2}Y)}}$ its joint characteristic function. How to find conditional characteristic function $${\varphi _{X\left| Y \right.}}(t) = {\rm{E}}\left( {\left. {{e^{itX}}} \right|Y} \right) $$ Could you recommend the textbook related to the task, please?
2026-03-26 19:25:21.1774553121
How to find conditional characteristic function if joint characteristic function is given?
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The task has been solved by M.S. Bartlett in his article "The Characteristic Function of a Conditional Statistic".