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# Probability functions

I am given a joint probability density function for X, Y, defined as f(x,y)=1, for 0≤x≤1,0≤y≤1, and 0 elsewhere. I need to find P(X−Y≤12).....how to solve using geometric approach ? how to solve using calculus approach? please elaborate your solution so that it is easy to understand.

also,can anyone post which books to refer for advanced probability and calculus at first year of bachelors level

p.s. i just passed my 12th and will start college soon.

Note by Rushikesh Joshi
2 years ago

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In the Cartesian plane, shade the region $$0 \leq x \leq 1, 0 \leq y \leq 1$$ with blue colour. You now have a blue square with area 1. Now shade the region $$x - y \leq 12$$ with red colour. $$P(X - Y \leq12)$$ is equal to the area of the region which is shaded red AND blue.

See that the entire square is shaded both red and blue, so $$P(X - Y \leq 12) = 1$$

Which college have you taken admission in? · 2 years ago