The square of a number x is 115. The number x is between what two consecutive whole numbers?
1 answer:
You might be interested in
Answer:
Step-by-step explanation:
1. Blue region. The boundary blue line passes through the points (0,-7) and (3,8), then its equation is
This line is solid, so the sign for the inequality should be with the notion "or equal to".
From the diagram you can see that the origin belongs to the blue region, then its coordinates satisfy the inequality. Thus,
2. Green region. The boundary green line passes through the points (6,-1) and (0,3), then its equation is
This line is solid, so the sign for the inequality also should be with the notion "or equal to".
From the diagram you can see that the origin doesn't belong to the blue region, then its coordinates satisfy the inequality. Thus,
3. The system of linear inequalities that represents these graphs is
Answer:
a)
So then we conclude that is an unbiased estimator of
So then we conclude that is an unbiased estimator of
b)
Step-by-step explanation:
For this case we know that we have two random variables:
both with mean
and variance
And we define the following estimators:
Part a
In order to see if both estimators are unbiased we need to proof if the expected value of the estimators are equal to the real value of the parameter:
So let's find the expected values for each estimator:
Using properties of expected value we have this:
So then we conclude that is an unbiased estimator of
For the second estimator we have:
Using properties of expected value we have this:
So then we conclude that is an unbiased estimator of
Part b
For the variance we need to remember this property: If a is a constant and X a random variable then:
For the first estimator we have:
Since both random variables are independent we know that so then we have:
For the second estimator we have:
Since both random variables are independent we know that so then we have: