3.1 + xCheck whether the following function is a valid pdf? If it is valid, obtain its CDF. If not valid,would scaling by a constant make it valid? If so, make it valid. Obtain its CDF? What is its mean?Variance?ƒ = —exp(-√x)U(x)

The given function: It must be checked if it's a pdf or not along with the way to make it valid if…

Answered: 3. Check whether the following function…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A regression was run to determine if there is a relationship between hours of TV watched per day (x) and number of situps a person can do (y). The results of the regression were: y=ax+b a=-1.271 b=39.101 ²-0.407044 r=-0.638 Assume the correlation is significant, and use this to predict the number of situps a person who watches 14 hours of TV can do (to one decimal place) Aft
In a regression analysis involving 30 observations, the following estimated regression equation was obtained. ŷ = 18.6 + 3.7x, - 2.2x2 + 7.9x3 + 2.6x4 (a) Interpret b, in this estimated regression equation. = 3.7 is an estimate of the change in y corresponding to a 1 unit change in x, when x,, x3, and x, are held constant. = -2.2 is an estimate of the change in y corresponding to a 1 unit change in x, when x2, x3, and x are held constant. O b1 = 7.9 is an estimate of the change in y corresponding to a1 unit change in x, when x,, x2, and x, are held constant. O b, O b, = 3.7 is an estimate of the change in y corresponding to a 1 unit change in x, = 2.6 is an estimate of the change in y corresponding to a 1 unit change in x, when x,, x2, and x3 are held constant. when and x4 are held constant. Interpret b, in this estimated regression equation. O b2 = 2.6 is an estimate of the change in y corresponding to a 1 unit change in x, when x,, x2, and x, are held constant. = 7.9 is an estimate…
A regression was run to determine if there is a relationship between hours of TV watched per day (x) and number of situps a person can do (y). The results of the regression were: y-ax+b a=-1.108 b-34.092 r2-0.736164 r=-0.858 Assume the correlation is significant, and use this to predict the number of situps a person who watches 4 区 hours q TV can do (to one decimal place) 72222392 口 D
Ocean currents are important in studies of climate change, as well as ecology studies of dispersal of plankton. Drift bottles are used to study ocean currents in the Pacific near Hawaii, the Solomon Islands, New Guinea, and other islands. Let x represent the number of days to recovery of a drift bottle after release and y represent the distance from point of release to point of recovery in km/100. The following data are representative of one study using drift bottles to study ocean currents. x days y km/100 71 76 31 92 203 14.2 19.6 5.8 11.2 35.9 (a) Verify that Ex = 473, Ey = 86.7, Ex = 61,451, Ey = 2033.69, Exy = 10995.7, and r 0.93868. %3D %3D %3D %3D Σχ 1 473 ΣΥ| 86.7 Ex2 61451 Ey2 2033.69 Exy 10995.7 r0.93868 (b) Use a 1% level of significance to test the claim p > 0. (Use 2 decimal places.) t 4.72 critical t 4.54 Conclusion Reject the null hypothesis, there is sufficient evidence that p > 0. O Reject the null hypothesis, there is insufficient evidence that p > 0. Fail to reject…
For variables X and Y we have that the correlation between them is 0.9. Also the standard deviation of Y is 8, while the standard deviation of X is 2. What is the slope of the regression equation that attempts to predict Y from X? Use two decimal places in your answer. Your Answer:
Consider a linear regression model for the decrease in blood pressure (mmHg) over a four-week period with muy=2.8+0.8x and standard deviation chi=3.2. The explanatory variable x is the number of servings fruits and vegetables in a calorie-controlled diet. Explain clearly what this slope says about the change in the mean of y for a change in x.
If our data were a perfect fit to our regression model, such that y; = ŷ;, we would expect | to be in the CI on p.
The variation of Y around its mean can be decomposed into which two parts?

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3. Check whether the following function is a valid pdf? If it is valid, obtain its CDF. If not valid, would scaling by a constant make it valid? If so, make it valid. Obtain its CDF? What is its mean? Variance? 1 ƒ = — exp(-√x)U(x) VX