A wss random process x(t) is applied to the input of an LTI system whose impulke response is 5 t · e-4, The mean of x(t) is 3. Find the mean of output of the system.
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- The variance of temperatures (Fahrenheit) in Denver, Colo. is 328.87. What is this variance if temp is re-expressed in Celsius? [Hint: Conversion between Fahrenheit and Celsius is a linear transformation: Fahrenheit = Celsius*1.80 + 32, or Celsius = Fahrenheit*(1/1.80) - (32/1.80)]The variance of temperatures (Fahrenheit) in Buffalo, N.Y. is 362.18. What is this variance if temp is re-expressed in Celsius? [Hint: Conversion between Fahrenheit and Celsius is a linear transformation: Fahrenheit = Celsius*1.80 + 32, or Celsius = Fahrenheit*(1/1.80) - (32/1.80)]A researcher collected a data set for a random sample of 930 individuals living in and around London, with data collected over 1-year period. The Table below reports the OLS coefficient estimates (intercept not reported) and standard errors (in parentheses), where the dependent variable is [100xIn(well-being)]. Commuting time/60 -0.267 (0.039) -0.14 (0.040) Age Age squared/100 0.12 (0.040) Hours worked -0.0053 (0.001) log real income 0.0267 (0.009) Married or cohabiting 0.589 (0.032) Num. of children. -0.051 (0.015) Saves Degree 0.299 (0.022) -0.022 (0.035) The explanatory variables are: Commuting time = Number of minutes of commuting time per day; Age= Age in years; Hours worked = Hours worked per week; Log of real household income = 100xLn(real household income measured in £10,000s); Num. of children = Number of children under the age of 18; Save regularly = 1 if save regularly, 0 otherwise; University degree = 1 if has a University degree, 0 otherwise. Calculate the test statistics…
- Plz solve it correctly I vill give 4 upvotes.Define the Distributed Lag Model with Additional Lags and AR(p) Errors?5. Oxygen demand is a term blologists use to describe the axygen needed by fish and other aquatic organisms for survval. The Environmental Protection Agency conducted a study of a wetland area in Marin County, Californla. In this wetland environment, the mean oxygen demand was u=9.9 mg/L, and a= 1.7 mg/L. (Reference: EPA Report 832-R- 93- 005). Let x be a random varlable that represents oxygen demand in this wetland environment. Assume x has a probability distribution that is approximately normal. a. An oxygen demand below 8 mg/L Indicates that some organisms In the wetland environment may be dying. What is the probability that the oxygen demand will fall below 8 mg/L? b. A high oxygen demand can also indicate trouble. An oxygen demand above 12 mg/L may indicate an overabundance of organisms that endanger some types of plant life. What is the probability that the oxygen demand will exceed 12 mg/L?
- A weight-loss program wants to test how well their program is working. The company selects a simple random sample of 51 individual that have been using their program for 15 months. For each individual person, the company records the individual's weight when they started the program 15 months ago as an x-value. The subject's current weight is recorded as a y-value. Therefore, a data point such as (205, 190) would be for a specific person and it would indicate that the individual started the program weighing 205 pounds and currently weighs 190 pounds. In other words, they lost 15 pounds. When the company performed a regression analysis, they found a correlation coefficient of r = 0.707. This clearly shows there is strong correlation, which got the company excited. However, when they showed their data to a statistics professor, the professor pointed out that correlation was not the right tool to show that their program was effective. Correlation will NOT show whether or not there is…Consider the following population model for household consumption: cons = a + b1 * inc+ b2 * educ+ b3 * hhsize + u where cons is consumption, inc is income, educ is the education level of household head, hhsize is the size of a household. Suppose a researcher estimates the model and gets the predicted value, cons_hat, and then runs a regression of cons_hat on educ, inc, and hhsize. Which of the following choice is correct and please explain why. A) be certain that R^2 = 1 B) be certain that R^2 = 0 C) be certain that R^2 is less than 1 but greater than 0. D) not be certainwhen using delta method to calculate variance, shouldn't [g'(μ)]^2 equal to (θ+1)^4?
- A random sample of n = 19 winter days in Denver gave a sample mean pollution index x1 = 43. Previous studies show that o1 = 10. For Englewood (a suburb of Denver), a random sample of n2 = 18 winter days gave a sample mean pollution index of x2 = 34. Previous studies show that o2 = 13. Assume the pollution index is normally distributed in both Englewood and Denver. Do these data indicate that the mean population pollution index of Englewood is different (either way) from that of Denver in the winter? Use a 1% level of significance. (a) What is the level of significance? State the null and alternate hypotheses. O Ho: H1 H2 O Ho: H1 = l2; H1: H1 < µ2 (b) What sampling distribution will you use? What assumptions are you making? O The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. O The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. O The Student's…I want to solve this. Help me plz.The variance of temperatures (Fahrenheit) in Las Vegas, Nev. is 327.84. What is this variance if temp is re-expressed in Celsius? [Hint: Conversion between Fahrenheit and Celsius is a linear transformation: Fahrenheit = Celsius*1.80 + 32, or Celsius = Fahrenheit*(1/1.80) - (32/1.80)]