The scale in Beatrice's bathroom gives readings which are normally distributed, with mean equal to the weight of the object placed on it

The scale in Beatrice's bathroom gives readings which are normally distributed, with mean equal to the weight of the object placed on it, and variance σ², which is unknown, and does not depend on the weight. Beatrice wishes to estimate σ². She places on the scale an object whose weight is known to be exactly 50 lbs, getting a reading Y₁. She repeats this independently n - 1 times, getting readings Y₁, Y₂,...,Y_n. She is considering the following two estimators of σ²:

Her reason for considering the second estimator is that she thinks that since she knows the true weight, she might as well use it, to get more accuracy. Which estimator is better, and does the answer depend on what is the true value of σ?

Expert Solution

Estimator A is better as it is unbiased while the estimator B is biased. here is a proof of why A is an unbiased estimatormof population variance-

Thanks!

orchestra answered 2 years ago

A 24.5 kg child sits on a bathroom scale which is placed on the seat of...

A 24.5 kg child sits on a bathroom scale which is placed on the seat of a swing. What does the scale read when the swing is at rest? The child begins to swing back and forth until she reaches a maximum height of 0.85 meters (measured vertically) above the low point. What will the scale read as she passes the low point? The swing rope is 3.0 meters long.

In the following exercises, assuming that the thermometer readings are normally distributed, with a mean of...

In the following exercises, assuming that the thermometer readings are normally distributed, with a mean of 0 celsius and a standard deviation of 1.00 celsius. A thermometer is randomly selected and tested. In each case, calculate the probability of each reading. a) P(z>1.645)

An instructor gives a 100-point test in which the grades are approximately normally distributed. The mean...

An instructor gives a 100-point test in which the grades are approximately normally distributed. The mean is 65 points and the standard deviation is 12 points. a. What is the lowest possible score to qualify in the top 5% of the scores? b. If 500 students took the test, how many students received a score between 60 and 80 points? ( I hope the solution to the questions can be provided as well )

Systolic blood pressure readings for females are normally distributed with a mean of 125 and a...

Systolic blood pressure readings for females are normally distributed with a mean of 125 and a standard deviation of 10.34. If 60 females are randomly selected then find the probability that their mean systolic blood pressure is between 122 and 126. Give your answer to four decimal places.

Assume that blood pressure readings are normally distributed with a mean of 124 and a standard...

Assume that blood pressure readings are normally distributed with a mean of 124 and a standard deviation of 9.6. If 144 people are randomly selected, find the probability that their mean blood pressure will be less than 126. Round to four decimal places.

Assume that blood pressure readings are normally distributed with a mean of 115 and a standard...

Assume that blood pressure readings are normally distributed with a mean of 115 and a standard deviation of 4.8. if 33 people are randomly selected, find the probability that their mean blood pressure will be less than 117.

Assume the readings on thermometers are normally distributed with a mean of 0°C and a standard...

Assume the readings on thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. Find the probability that a randomly selected thermometer reads between -2.05 and −1.18

Blood pressure readings are normally distributed with a mean of 120 and a standard deviation of...

Blood pressure readings are normally distributed with a mean of 120 and a standard deviation of 8. a. If one person is randomly selected, find the probability that their blood pressure will be greater than 125. b. If 16 people are randomly selected, find the probability that their mean blood pressure will be greater than 125. 5 c. Why can the central limit theorem be used in part (b.), even that the sample size does not exceed 30?

Assume that blood pressure readings are normally distributed with a mean of 123 and a population...

Assume that blood pressure readings are normally distributed with a mean of 123 and a population standard deviation of 9.6. If 67 people are randomly selected, find the probability that their mean blood pressure will be less than 125.

The mass of an object is normally distributed with a mean of μ = 3480 grams...

The mass of an object is normally distributed with a mean of μ = 3480 grams and a standard deviation of σ = 550 grams. Find the 28th percentile in this population. a. 3161 grams b. 2834 grams c. 3050 grams d. 2824 grams Part B.) If five objects from the population are randomly selected, what is the probability the mean mass among them is less than 3229 grams? a.) 0.1539 b.) 0.4020 c.) 0.546 d.) 0.0250

Question