You are a birdwatcher listening for bird calls in a quiet park on a peaceful April day.Based on your experience, you hear an average of one bird call per minute. Also, when youhear a bird call, it’s a robin 12of the time, a woodpecker 13of the time, and a sparrow 16ofthe time.Assuming that three types of bird calls are independent Poisson processes, identify the distributions of the following random variables: give the name of the distribution and its parameters.(a) W is the time it takes you to hear a woodpecker call.(b) R is the number of robin calls you hear over the course of an hour.(c) T is the time it takes you to hear 10 bird calls total.(d) After you’ve heard 10 bird calls total, S is the number of sparrow calls you’ve heard.
You are a birdwatcher listening for bird calls in a quiet park on a peaceful April day.
Based on your experience, you hear an average of one bird call per minute. Also, when you
hear a bird call, it’s a robin 1
2
of the time, a woodpecker 1
3
of the time, and a sparrow 1
6
of
the time.
Assuming that three types of bird calls are independent Poisson processes, identify the distributions of the following random variables: give the name of the distribution and its parameters.
(a) W is the time it takes you to hear a woodpecker call.
(b) R is the number of robin calls you hear over the course of an hour.
(c) T is the time it takes you to hear 10 bird calls total.
(d) After you’ve heard 10 bird calls total, S is the number of sparrow calls you’ve heard.
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