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cody665
19.03.2020 •
Mathematics
Suppose rain is falling at an average rate of 30 drops per square inch per minute. What is the chance that a particular square inch is not hit by any drops during a given 10-second period? What assumptions are you making?
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Ответ:
Using the Poisson distribution, and considering that intervals are independent, it is found that there is a 0.0067 = 0.67% probability that a particular square inch is not hit by any drops during a given 10-second period.
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:
The parameters are:
x is the number of successes e = 2.71828 is the Euler numberIn this problem, the rate is of 30 drops per minute, hence, for 10 seconds, considering intervals are independent, the mean is:
The probability that a particular square inch is not hit by any drops during a given 10-second period is P(X = 0), hence:
0.0067 = 0.67% probability that a particular square inch is not hit by any drops during a given 10-second period.
A similar problem is given at link
Ответ:
Therefore the chance that a particular square inch is not by any drops during a given 10 second period is
.
Step-by-step explanation:
Poisson distribution:
Given that rain is falling at an average rate 30 drops per square inches per minutes.
A reasonable choose of this distribution is Poisson distribution
.
Let the area be a square inch.
Here
= average rate of rain drop × area
=(30×a)= 30 a
t = 10 second
.
Therefore,
Therefore the chance that a particular square inch is not by any drops during a given 10 second period is
.
Ответ:
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