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Question Number 75524 by mhmd last updated on 12/Dec/19
$${Suppose}\:{that}\:{X}\:{and}\:{Y}\:{have}\:{a}\:{discrete}\:{joint}\:{distribution}\:{for}\:{which}\:{the}\:{joint}\:{p}.{f}\:\:{is}\:{defined}\:{as}\:{follows}\: \\ $$$${f}\left({x},{y}\right)=\left\{\:{c}\mid{x}+{y}\mid\:{for}\:{x}=−\mathrm{2},−\mathrm{1},\mathrm{0},\mathrm{1},\mathrm{2}\:{and}\:{y}=−\mathrm{2},−\mathrm{1},\mathrm{0},\mathrm{1},\mathrm{2}\right. \\ $$$$\mathrm{0}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{other}\:{wise} \\ $$$${Determine}\:\left({a}\right)\:{the}\:{value}\:{of}\:{the}\:{constant}\:{of}\:{c} \\ $$$$\left({b}\right)\:{pr}\left({X}=\mathrm{0}\:{and}\:{Y}=−\mathrm{2}\right) \\ $$$$\left({e}\right)\:{pr}\left({X}=\mathrm{1}\right) \\ $$$$\left({d}\right)\:{pr}\left(\mid{x}−{y}\mid\leqslant\mathrm{1}\right) \\ $$$${pleas}\:{sir}\:{help}\:{me} \\ $$