Let Y have the density function f(y) = ke−2y for all y > 0 and zero...

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Let Y have the density function f(y) = ke−2y for all y > 0 and zero...

Let Y have the density function f(y) = ke−2y for all y > 0 and zero everywhere else. Find the value of k that makes f(y) a probability density function.

a. Calculate P(0.5 ≤ Y ≤ 1) and P(0.5 ≤ Y < 1).

b. Calculate P(0.5 ≤ Y ≤ 1|Y ≤ 0.75) and P(0.5 ≤ Y ≤ 1|Y < 0.75).

math Statistics-And-Probability

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Answer 1

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fly) = kely ot otherwire (f(y) dy = 4 ** like 24 dy = 1 k Let at K=2 a) P6053451) a szedy = 3(-ete] = (-0.1353 + 0.3670] = ons va b) (0,5 < < ( 114 0.7s); T ze dy 0.5 0.75 z 10-24 E -p2(0.75) 4 2 260.5) = 0.1447 PC0.5 Sysily<0.75) = 0.1447 In conti

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Let Y have the density function f(y) = ke−2y for all y > 0 and zero...

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Let Y have the density function f(y) = ke−2y for all y > 0 and zero...

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