Twice the sum of a number and 2 is equal to three times the difference of the number and 7.Find the number.
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Answer is in the attachment below.
Answer:
And then the maximum occurs when , and that is only satisfied if and only if:
Step-by-step explanation:
For this case we have a random sample where
where
is fixed. And we want to show that the maximum likehood estimator for
.
The first step is obtain the probability distribution function for the random variable X. For this case each have the following density function:
The likehood function is given by:
Assuming independence between the random sample, and replacing the density function we have this:
Taking the natural log on btoh sides we got:
Now if we take the derivate respect we will see this:
And then the maximum occurs when , and that is only satisfied if and only if: