(a) Find the probability Pr(X s x, Y = y) (b) Find the probability Pr(X s x- 1, Y = y) (c) Find the probability Pr(X = x, Y = y)

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A: we use Trigonometry table to find out values of y = sin(2x)

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A: Total female = 133+43 = 178 Total "did not graduate" = 55+43 = 98 Grand total= (126+55+133+43)  =…

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A: We will evaluate the required value.

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A: Given expression: 2+2

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A: Expanding:                             (1x-2x)5   We can expand this expression using binomial…

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Q: 2. Evaluate dz.

A: I = ∫x31 - x2 dxLet, x = cosθ ⇒ dx = -sinθ dθSo, I = ∫cos3θ1 - cos2θ- sinθ dθ          = - ∫cos3θ…

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A: Given: I=4θ2-25dθ We know that ∫x2-a2dx=x2x2-a2-a22logx+x2-a2+c…

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A: here the graph passes two times  through the x -axis  so there will be two roots

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