A transport company needs to deliver 300 pounds of rocks to a construction site. The company owns a set of dump trucks- each wit
h a container in the shape of a rectangular prism (figure A). If each pound of rock has a mass of 8 cubic feet, how many dump trucks will it take to transport the rock?
Calculate the total volume of rock that the transport company is responsible for.
Calculate the maximum volume of each dump truck.
How many trucks are needed to deliver the rock in one trip?
Calculate the total volume of rock that the transport company is responsible for.
Calculate the maximum volume of each dump truck.
How many trucks are needed to deliver the rock in one trip?
2 answers:
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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: