9 10 11 `1
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There is an overlap between the two periods. Since each individual function is uniform, the resulting f(x) is a step function such that:
f(x): (1/4)/2 = 1/8 for x∈[9,10]
f(x): (1/4)/2+(3/4)/2 = 1/2 for x∈[10,11]
f(x): (3/4)/2 = 3/8 for x∈[11,12]
∫xf(x) = 1/8+1/2+3/8=1 checks.
On any given day, mail gets delivered by either Alice or Bob. If Alice delivers it, which happens with probability 1/4, she does so at a time that is uniformly distributed between 9 and 11. If Bob delivers it, which happens with probability 3/4, he does so at a time that is uniformly distributed between 10 and 12. The PDF of the time X that mail gets delivered satisfies
a) fX(9.5)=
b) fX(10.5)=
2 answers
a) 0.125
b) 0.5
b) 0.5
1 answer