19. (a) Define the joint distribution and joint distribution function of a bivariate ran- dom variable. (b) Define its marginal distributions and marginal distribution functions. (c) Explain how to compute the marginal distribution functions from the joint distribution function.
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- If(x,y)-N(0,-11,4,0.5),the marginal distribution of X- Y-Weekly downtime of internet services from an internet service provider (in hours) has expected value 0.5 and variance 0.25. Based on past experience, the data scientist of a retailer store has calculated the loss function to the store from the downtime as C=30X+2X2 where X is the amount of weekly downtime and C is cost. Find the Expected cost, i.e, E(C).Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 50 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that ? = 7.00 ml/kg for the distribution of blood plasma. (a) Find a 99% confidence interval for the population mean blood plasma volume in male firefighters. What is the margin of error? (Round your answers to two decimal places.) lower limit upper limit margin of error (b) What conditions are necessary for your calculations? (Select all that apply.) n is large ? is unknown the distribution of volumes is normal the distribution of volumes is uniform ? is known (d) Find the sample size necessary for a 99% confidence level with maximal margin of error E…
- Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 50 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that ? = 7.00 ml/kg for the distribution of blood plasma. (a) Find a 99% confidence interval for the population mean blood plasma volume in male firefighters. What is the margin of error? (Round your answers to two decimal places.) lower limit= upper limit= margin of error= (b) What conditions are necessary for your calculations? (Select all that apply.) the distribution of volumes is uniformt he distribution of volumes is normal ? is known n is large ? is unknown (c) Interpret your results in the context of this problem. We are 99% confident that the true average…The residual plot shows the residuals for the least- squares line relating price of a used car (y) to the number of miles driven (x). Residuals Residual Plot for Miles Driven vs Price 10,000 5,000 -5,000 50,000 100,000 150,000 200,000 Number of Miles Driven Based on the residual plot, is the linear model appropriate for the relationship between miles and price? No, because there are clear outliers in the residual plot. No, because there is a clear curved pattern in the residual plot. No, because there does not appear to be a pattern to the residuals. Yes, because there is a clear curved pattern in the residual plot. Yes, because there does not appear to be a pattern to the residuals.Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 42 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that ? = 8.00 ml/kg for the distribution of blood plasma. (a) Find a 99% confidence interval for the population mean blood plasma volume in male firefighters. What is the margin of error? (Round your answers to two decimal places.) lower limitupper limitmargin of error (b) What conditions are necessary for your calculations? (Select all that apply.) the distribution of volumes is uniform? is knownn is largethe distribution of volumes is normal? is unknown (c) Interpret your results in the context of this problem. We are 99% confident that the true average blood…
- Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 40 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that ? = 7.80 ml/kg for the distribution of blood plasma. (d) Find the sample size necessary for a 99% confidence level with maximal margin of error E = 2.00 for the mean plasma volume in male firefighters. (Round up to the nearest whole number.) male firefightersTotal plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 48 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that ? = 7.00 ml/kg for the distribution of blood plasma. (a) Find a 99% confidence interval for the population mean blood plasma volume in male firefighters. What is the margin of error? (Round your answers to two decimal places.) lower limit =______ upper limit =______ margin of error = _______ (b) What conditions are necessary for your calculations? (Select all that apply.) the distribution of volumes is normal the distribution of volumes is uniform ? is known ? is unknown n is large (d) Find the sample size necessary for a 99% confidence level with maximal…Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 46 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that ? = 7.80 ml/kg for the distribution of blood plasma. (d) Find the sample size necessary for a 99% confidence level with maximal margin of error E = 2.90 for the mean plasma volume in male firefighters. (Round up to the nearest whole number.) ________ male firefighters
- Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 50 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that ? = 7.20 ml/kg for the distribution of blood plasma. (d) Find the sample size necessary for a 99% confidence level with maximal margin of error E = 2.50 for the mean plasma volume in male firefighters. (Round up to the nearest whole number.) ______ male firefightersTotal plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 43 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that ? = 8.00 ml/kg for the distribution of blood plasma. (a) Find a 99% confidence interval for the population mean blood plasma volume in male firefighters. What is the margin of error? (Round your answers to two decimal places.) lower limit ___ upper limit ___ margin of error ___ (b) What conditions are necessary for your calculations? (Select all that apply.) A-? is known B-the distribution of volumes is uniform C-? is unknown D-n is large E-the distribution of volumes is normal (d) Find the sample size necessary for a 99% confidence level with maximal…Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 44 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that ? = 7.20 ml/kg for the distribution of blood plasma. (a) Find a 99% confidence interval for the population mean blood plasma volume in male firefighters. What is the margin of error? (Round your answers to two decimal places.)lower limit= upper limit= margin of error= (b) What conditions are necessary for your calculations? (Select all that apply.) the distribution of volumes is normal ? is known the distribution of volumes is uniform n is large ? is unknown c) Find the sample size necessary for a 99% confidence level with maximal margin of error E = 2.80 for the mean plasma…