Question

Let X be exponentially distributed with parameter 3.

a) Compute P(X > 6 | X > 2).

b) Compute E(7e^-12x+8+ 5).

c) Let Y be independent from X. Suppose the PDF for Y is f(x) = 2x for 0 ≤ x ≤ 1 (and 0 else). Find the PDF of X + Y.

Answer 1

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PASES I Page 3 Cheaal $ ca P[x76\x72J = 6.144212353x10-6 =0.000006144212 353 So I Le 12*+*+5]. E le 12te] +5. - Fietus blandit ts G12x+8 3e 31 dx +5 so 120-18-30 dx +5 o co 15x+8 do +5 1e

T Page 4 cheap I Page 41 8b). -1578 dx +5 + S -70[2+1+5 = 700 [°-17 to. - see +5. 2798 +5 + BC = 4178.34182

I Page 5 Page 5 - Cheap 9002 E le 2x+8+5] 54178.341182. Let us de tine U = aty. osy. . » na uro yao Noot (4,0) blacy) lJ. where J-Jacobian of the trane formation . x

Page 6 - Cheap I T Page 6] . 6 (4,9)= 3е зи-) 2 Поо аmе o6 49- с. .: + 4) = (+) до 3r dur - Зее 2 | e = Be-34 Г. re — ве за Гсело — «» у] - -* г. - «*»). = be Love» — не – еве «Lertv-Т.

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