Asked by sagar
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)=
a) fX(9.5)=
b) fX(10.5)=
Answers
Answered by
MathMate
9 10 11 `1
********
********
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.
********
********
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.
Answered by
Zorry
a) 0.125
b) 0.5
b) 0.5
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.