Answer:
The solution is in the attached file
Step-by-step explanation:
Choose the examples you would like to use from the examples listed for both true and false
Three candidates run for different offices in different cities. Each has a one in three chance of being elected in his/her city.
1 answer:
You might be interested in
Answer:
Bias for the estimator = -0.56
Mean Square Error for the estimator = 6.6311
Step-by-step explanation:
Given - A normally distributed random variable with mean 4.5 and standard deviation 7.6 is sampled to get two independent values, X1 and X2. The mean is estimated using the formula (3X1 + 4X2)/8.
To find - Determine the bias and the mean squared error for this estimator of the mean.
Proof -
Let us denote
X be a random variable such that X ~ N(mean = 4.5, SD = 7.6)
Now,
An estimate of mean, μ is suggested as
Now
Bias for the estimator = E(μ bar) - μ
=
=
=
=
=
= 3.9375 - 4.5
= - 0.5625 ≈ -0.56
∴ we get
Bias for the estimator = -0.56
Now,
Mean Square Error for the estimator = E[(μ bar - μ)²]
= Var(μ bar) + [Bias(μ bar, μ)]²
=
=
=
=
=
=
=
= 6.6311
∴ we get
Mean Square Error for the estimator = 6.6311
Answer:
The height (in feet) at which the laser will impact the wall is 6.75 feet
Step-by-step explanation:
The given parameters are;
The height from which the laser beam operator is holding the laser = 9 feet
The horizontal distance away from the pointer the beam is reflected = 8 feet
Given that we have;
When x = 8, the point of reflection, the height, f(x) is given as follows;
When x = 7, the point of reflection, the height, f(x) is given as follows;
Therefore, given that the point of reflection is at an elevation of 0 relative to the 9 feet of the laser source (pointer), by tan rule, we have;
Where;
h = The height at which the laser meets the wall
Given that the wall the laser meets is at the point x with elevation 9/8, the height, y, at which the laser meets the wall is therefore;
The height (in feet) at which the laser will impact the wall = 6.75 feet.