Today, the waves are crashing onto the beach every 5.8 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 5.8 seconds. Round to 4 decimal places where possible.The probability that it will take longer than 1.96 seconds for the wave to crash onto the beach after the person arrives is P(x ≥≥ 1.96) = Find the minimum for the upper quartile.  seconds

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Asked Nov 2, 2019
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Today, the waves are crashing onto the beach every 5.8 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 5.8 seconds. Round to 4 decimal places where possible.

The probability that it will take longer than 1.96 seconds for the wave to crash onto the beach after the person arrives is P(x ≥≥ 1.96) = 

Find the minimum for the upper quartile.  seconds

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Expert Answer

Step 1

The probability density function (PDF) of the uniformly distributed random variable with parameters (a, b) is:

 

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1 asxsb f(x)b-a |0, otherwise. 1 0Sx5.8 f (x)={5.8-0 0. That is otherwise 1 0 < x< 5.8 f(x)5.8 |0, otherwise

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Step 2

Computing the probability that longer than 1.96 seconds takes for the wave to crash onto the beach after the person arrives, P(X>1.96 seconds):

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5.8 P(X>1.96) ()ck 5.8 1 dx 1.96 5.8 1 5.8 dx 5.8 J196 1 1.96 5.8 1 (5.8-1.96) 5.8 3.84 5.8 0.6621

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Step 3

The cumulative distribution function (CDF) of the uniform distribution:

If X is a uniformly distributed random variable between consta...

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0. ifx <a if asx <b b-a P(X<x) if x 2 b | 1,

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Hypothesis Testing

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