prob stat: The p.d.f of a discrete r.v. Y is given by P(Y=y)=cy^2 for y=0,1,2,3,4.

Let f(x) be a polynomial of degree 1. If f(10)-f(5)=15, then f(20)-f(5)=?

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A box contains 8 blue & 6 red socks. What is the number of ways that 2 socks can be drawn ...

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alternate way: count sum 1 + 2 + 3+... + n via "polynomial"

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Alternate way: Find 1+2+3+... +(n-1)+n via "polynomial degree 2"

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2 ways: trig show tan(2x)=2tan(x)/1-tan^2(x))

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2nd/3ways: Laplace Show that ...

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Screen Recording 2024-05-10 at 6.19.39 PM

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2nd way: integral ∫x^2/(x^3 -2)^5 dx

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integration bee 2018 Swinburne U integral x^2/2 ln(2/x^2) dx

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