A biased weather forecaster makes daily predictions about the temperature, in degrees Fahren- heit, at a...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
A biased weather forecaster makes daily predictions about the temperature, in degrees Fahren- heit, at a station at noon each day. Let random variable W represent the forecast error for any given day. For example, if the forecast is 89.1 degrees and the actual temperature is 90.1 degrees, -1.0. Assume W follows a normal distribution with mean 1.5 and then we would have W standard deviation 6.2. (a) (1 point) Explain in one or two sentences why this forecaster is considered "biased." (b) (2 points) Calculate the probability that the next forecast will miss on the low side, i.e., P(W < 0). Set up the relevant integral and then use R to make the calculation. Write the R code necessary to get the answer. (c) (4 points) A different forecaster of temperatures at the same station has error distribution N(1.9, sd=3.0). This forecaster's predictions are further off, on average, but they are less variable. Suppose the criterion for judging a forecaster is the probability of getting a forecast within five degrees of the truth (i.e., P(|error| < 5)). Using this criterion, determine which of the two forecasters is preferred. Include your R code. U (d) (2 points EXTRA CREDIT) Calculate the probability that the first forecaster (with daily error W) will miss at least three of their next five forecasts on the low side. Assume each forecast error independently follows the same normal distribution with mean 1.5 and standard deviation 6.2. A biased weather forecaster makes daily predictions about the temperature, in degrees Fahren- heit, at a station at noon each day. Let random variable W represent the forecast error for any given day. For example, if the forecast is 89.1 degrees and the actual temperature is 90.1 degrees, -1.0. Assume W follows a normal distribution with mean 1.5 and then we would have W standard deviation 6.2. (a) (1 point) Explain in one or two sentences why this forecaster is considered "biased." (b) (2 points) Calculate the probability that the next forecast will miss on the low side, i.e., P(W < 0). Set up the relevant integral and then use R to make the calculation. Write the R code necessary to get the answer. (c) (4 points) A different forecaster of temperatures at the same station has error distribution N(1.9, sd=3.0). This forecaster's predictions are further off, on average, but they are less variable. Suppose the criterion for judging a forecaster is the probability of getting a forecast within five degrees of the truth (i.e., P(|error| < 5)). Using this criterion, determine which of the two forecasters is preferred. Include your R code. U (d) (2 points EXTRA CREDIT) Calculate the probability that the first forecaster (with daily error W) will miss at least three of their next five forecasts on the low side. Assume each forecast error independently follows the same normal distribution with mean 1.5 and standard deviation 6.2.
Expert Answer:
Related Book For
Posted Date:
Students also viewed these mathematics questions
-
If x has a normal distribution with mean = 15 and standard deviation = 3, describe the distribution of values for sample size n, where n = 4, n = 16, and n = 100. How do the x distributions compare...
-
The function g(x) = 23(0.94)x gives the temperature in degrees Celsius of a bowl of water x minutes after a large quantity of ice is added. After how many minutes will the water reach 5C?
-
For the normal distribution with mean 70 and standard deviation 12, find: (a) Pr(73 x 97) (b) Pr(65 x 84) (c) Pr(x > 84)
-
The cost of a can of Coca Cola in 1960 was $0.10. The exponential function that models the cost of a Coca Cola by year is given below, where t is the number of years since 1960. C(t) = 0.10e0.0576t...
-
Read the Tax Court of Canada case Min Shan Shih v the Queen 2000 DTC 2072 and explain in your own words the reason for the decision in the case.
-
Shown below is information from the financial reports of Knauss Supermarkets for the past few years. Instructions a. Calculate the following statistics for Knauss Supermarkets (round your answers to...
-
Police in Albemarle County, Virginia, were on the lookout for a stolen orange and black motorcycle that had eluded them in two previous traffic incidents. Officer David Rhodes drove past the home of...
-
The Hoylake Rescue Squad receives an emergency call every 1, 2, 3, 4, 5, or 6 hours, according to the following probability distribution: Time Between emergency Probability Calls (hours) 1...
-
At some point in the life of a company or firm, a decision of how to expand is necessary. This is especially important in for-profit firms as shareholders typically require larger and larger...
-
Given the accompanying sample data, use Excels formula options to find the 99% confidence interval for the population mean. Assume that the population is normally distributed.
-
Your company produces an assortment of school supplies, and has a policy of supporting child health. One day you happen to notice information that (although it is not your area of expertise), in your...
-
What is the ex-dividend date, and why is it important to investors?
-
Is it always necessary to adjust projects cash flows when different projects have unequal lives? Explain.
-
Explain the procedures used to actually pay the dividend.
-
Should all divisions within the same firm use the firms composite WACC for evaluating all capital budgeting projects? Explain.
-
Differentiate between independent and mutually exclusive projects.
-
You are in a Board of Directors meeting when a senior board member turns to you and asks, "What are the conditions that indicate that an innovation or product innovation is about to become, or is...
-
Marc Company assembles products from a group of interconnecting parts. The company produces some of the parts and buys some from outside vendors. The vendor for Part X has just increased its price by...
-
Use Property 11 to estimate the value of the integral. T is the triangle enclosed by the lines y = 0, y = 2x, and x = 1 || sin*(x + y) dA,
-
Find the Maclaurin series for f (x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do not show that R n (x) 0.] Also find the associated radius of...
-
(a) Write expressions for the partial derivatives f x (a, b) and f y (a, b) as limits. (b) How do you interpret f x (a, b) and f y (a, b) geometrically? How do you interpret them as rates of change?...
-
An engineering organisational system is composed of major groups such as management, research and development, preliminary design, experiments, product design and drafting, fabrication and...
-
The student-teacher learning activity is inherently a feedback exercise intended to reduce the system error to a minimum. The desired output is the knowledge being studied, and the student is the...
-
Give two examples of feedback control systems in which a human acts as a controller.
Study smarter with the SolutionInn App