Let x1, x2, , xn be a random sample from n(μ, σ2), where the mean θ = μ is such that −[infinity] < θ < [infinity] and σ2 is a known positive number. show that the maximum likelihood estimator for θ is θ^ = x.

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:

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.

i think is g(1)=-1.

hope that i can