Choose two numbers X and Y uniformly from the interval [0, 1]. ) Find the probability that max{X, Y} < 1/2. -) Find the probability that X2 + Y² < 1. ) Find the probability that XY < 1/2.

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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Choose two numbers X and Y uniformly from the interval [0, 1].
a) Find the probability that max{X, Y} < 1/2.
b) Find the probability that X2 + Y2<1.
c) Find the probability that XY < 1/2.
Transcribed Image Text:Choose two numbers X and Y uniformly from the interval [0, 1]. a) Find the probability that max{X, Y} < 1/2. b) Find the probability that X2 + Y2<1. c) Find the probability that XY < 1/2.
In preparing a report on the economy, we need to estimate the percentage of businesses that plan to hire additional employees in
the next 60 days.
a) How many randomly selected employers must we contact in order to create an estimate in which we are 95% confident with a
margin of error of 9%?
b) Suppose we want to reduce the margin of error to 4%. What sample size will suffice?
c) Why might it not be worth the effort to try to get an interval with a margin of error of 1%?
a) A sample size of
(Round up to the nearest whole number.)
is needed.
Transcribed Image Text:In preparing a report on the economy, we need to estimate the percentage of businesses that plan to hire additional employees in the next 60 days. a) How many randomly selected employers must we contact in order to create an estimate in which we are 95% confident with a margin of error of 9%? b) Suppose we want to reduce the margin of error to 4%. What sample size will suffice? c) Why might it not be worth the effort to try to get an interval with a margin of error of 1%? a) A sample size of (Round up to the nearest whole number.) is needed.
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