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Median [special weighted mean]
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Penn. State U: Suppose the p.m.f of discrete random variable X is ...
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example: Mean, Median & Mode
trig Write each expression as an equivalent algebraic expression involving only x.
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🪔 Happy Deepavali 🪔 [Nov-12-2023]
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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx
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MP 98 Hindustan: Evaluate (i) ∫e^loge(x) dx (ii) ∫e^(-loge(x)) dx
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AI 2008 Hindustan 2nd/2 ways: Evaluate trig integral ∫2cos(x)/(3 sin^3(x)) dx
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count quick review: Permutation vs Combination
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Alternate way: Find 1+2+3+... +(n-1)+n via "polynomial degree 2"
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diff eq: Solve dy/dx = (2y4x^4)/(xy^3) ❌separable to ✅separable
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2nd/2ways: count perm Show P(n,n)=P(n,n-1)
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2 ways: trig Show (1-cos(x))/sin(x)=sin(x)/(1+cos(x))
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trig Show these identities ...
2nd way: derivative y=e^x sin(x) cos^3(x)
A cubical die, numbered 1 to 6 is weighted so that a six is twice as likely to occur as any other #.
NUS MA1102R: For f(x,y) = e^(xy) + x/y, compute fx & fy
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Lamar U: Differentiate ... a) (5x^3-7x+1)^5 [f(x)]^5, [y(x)]^5
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Bijection of elements in tn & a pair of elements of (n+1)
trig integral ∫arc sin(x)/√(1-x^2) dx vs ∫1/(arc sin(x) √(1-x^2)) dx