Mr. Webb gave his waiter a $8.60 tip on a $50 bill. What percent did he give the waiter?
2 answers:
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Answer:
tex]M=\beta ln(2)[/tex]
Step-by-step explanation:
Previous concepts
The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate).
Solution to the problem
For this case we can use the following Theorem:
"If X is a continuos random variable of the exponential distribution with parameter for some
"
Then the median of X is
Proof
Let M the median for the random variable X.
From the definition for the exponential distribution we know the denisty function of X is given by:
Since we need the median we can put this equation:
If we evaluate the integral we got this:
And that's equal to:
And if we solve for M we got:
If we apply natural log on both sides we got:
And then