3) The probability density function for Y is given by -7₁ e y > 0 (0, elsewhere f(y) = 30 And its cumulative distribution function is given by F(y) = {1-e%, y > 0 0, elsewhere a) Use the cumulative distribution method or transformation method to show that is a pivotal quantity. (6)

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A: 3) From the given information, X≈b(8, 14) E(X)=8*14=2 Consider, E5+6x=5+6E(X)…

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A: a) The expectation is calculated as follows: EX=∫01x6x-x2dx=∫016x2-x3dx=6x33-x4401=613-14=612=12

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A: It is an important part of statistics. It is widely used.

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Q: (47) Let X b(8, -) find E(5+6x) and distribution function.

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