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Elza [17]
3 years ago
9

Two students, A and B, are working independently on homework (not necessarily for the same class). Student A takes X = Exp(1) ho

urs to finish his or her homework, while B takes Y = Exp(2) hours. (a) Find the CDF of X/Y , the ratio of their problem-solving times. (b) Find the probability that A finishes his or her homework before B does.

Mathematics
1 answer:
OleMash [197]3 years ago
7 0

Answer:

a) The CDF of X/Y is calculated as:

F_{z} (\zeta) = \frac{\zeta}{\zeta + 2} for 0 < \zeta < \infty  

F_{z} (\zeta) = 0 for \zeta \leq 0

Note: Z = X/Y

b) Probability that A finishes before B = 1/3

Step-by-step explanation:

For clarity and easiness of expression, this solution is handwritten and attached as a file. Check the complete solution in the attached file.

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I don't know what I'm doing wrong here, can anyone help?
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if you look at the part where the first part connects with the second part:

y = 5 if x < - 2

y = -2x + 1 if  -2 ≤ x < 1

we don't have a discontinuity there, so there shouldn't be a dot.

<h3></h3><h3>What is wrong with the graph?</h3>

When we graph over intervals like (a, b) or [a, b] or something like that, we use dots to define the end of the intervals, and to denote that the function ends abruptly or we have a jump.

In this case, you can see that between the end and the second part and the beginning of the third part there is a jump, so the use of dots is correct there, but if you look at the part where the first part connects with the second part:

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y = -2x + 1 if  -2 ≤ x < 1

we don't have a discontinuity there, so there shouldn't be a dot.

That is the only error with the graph.

If you want to learn more about piecewise functions:

brainly.com/question/3628123

#SPJ1

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Answer:

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Step-by-step explanation:

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