Question:

Community ecologists draw "food webs" to describe the predator and prey relationships between all organisms living in an area. A theoretical model predicts that a measure of the structure of food webs called "diet discontinuity" should be zero. Diet discontinuity is a measure of the relative numbers of predators whose prey are not ordered contiguously. Researchers have measured discontinuity scores for seven different food webs in nature. The values are: 0.35, 0.08, 0.004, 0.08, 0.32, 0.28, 0.17. Assume discontinuity in natural food webs has a normal distribution. Are the results significantly different from the theoretical expectation? Answer TRUE for 'yes' and FALSE for 'no'.

True

False

2.As the world warms, geographic ranges of species might shift toward cooler areas. In the file 'RangeShiftsWithClimateChange.csv' are data from a study on the highest elevations at which species occur. Typically, higher elevations are cooler than lower elevations. The aforementioned file contains data in the changes in highest elevation for 31 taxa in meters between the late 1990's and the early 2000's. Positive numbers indicate upward shifts in elevation and negative numbers indicate shifts to lower elevations. Based on this information, the mean altitude shift is , the lower 95% confidence limit is , and the upper 95% confidence limit is . Please round your answers to zero decimal places (i.e., only provide rounded numbers to the left of where the decimal point would go).

3.Assume that Z is a number randomly chosen from a standard normal distribution. Use R to calculate P[Z

4.The babies born in singleton births in the United States have birth weights that are approximately normally distributed with mean 3.296 kg and standard deviation 0.560 kg. What is the probability of a newborn weighing between 3 and 4 kg? Round your answer to two decimal places.

5.It was rumored that Britain's domestic intelligence service, MI5, has an upper limit on the height of its spies, on the assumption that tall people stand out. The rumor also said that to be a spy, you could be no taller than 5 feet 11 inches (180.3 cm) if you are a man. If the true mean height of men in Britain is 177 cm and the true standard deviation is 7.1 cm, what fraction of men would be precluded from applying to MI5? Please round your answer to two decimal places.

6.Can a human swim faster in water or in syrup? It is unknown whether the increase in the friction of the body moving through syrup is compensated by the increased power of each stroke. The results of an experiment in which researchers filled one pool with water mixed with syrup and another with normal water are in the file 'SyrupSwimming.csv'. The data are presented as the relative speed of each swimmer in syrup (i.e., speed in syrup / speed in water). If syrup has no effect on swimming, the mean should be one. Assuming these data are normally distributed, use this information to test the null hypothesis that syrup has no effect on swim peed. Answer TRUE if syrup does have a statistically significant effect and FALSE if the test fails to reject the null hypothesis.

Spring 2018 ECE 103 Engineering Programming These are some important parameters that characterize the Gaussian beam: . Rayleigh range: Z Minimum beam waist (aka minimum spot size) at location z = 0: w. Beam width at position z along the beam axis: w(z) . Beam angular spread (radians): 0 = 26, where 8 4 Note: A is the beam wavelength To make a functioning laser, curved mirrors are placed along the axis to create a resonant cavity that reflects the beam back and forth. If the two mirrors have radii of curvature Ri and Ra. respectively, they need to be placed at specific locations z, and zz along the axis to exactly match the wavefront's radius at those locations (Figure 3). :=0 Figure 3: Two-mirror resonant cavity" Suppose you are given two mirrors with radii Ri and Ra. They are to be placed a distance & apart. Where are the mirror locations 21 and zz? The locations can be calculated from these equations: L(R, - L) R, + RX - 2L The Kayleigh length Z, is then: L(R, - L)(R, - LYR + R2 - L) ]3 (R, + Rx - 21] Assuming index . = 1, the minimum beam waid w, is given by: where 8, =1 - and 83 =1- L Source Later Physics, M. Sargent III, M. L. Scully. W. F. Larob Jr, Addison Wesley (1977)28. Making decisions based on probability involves: a) Descriptive Statistics b) Statistical Inference c) Conditional Probability d) Response bias 29. Which of the answers below are methods of Power transformation? a) Square root, Cube root, Logarithm b) Median, Mode, Mean c) Slope, y-intercept d) None of the above1. Determine the mean-square value of the random process with spectral density defined by: Sx (w) = 1 - 2. Consider a random process with spectral density Sx (@)). The process has mean-square value of 4. Determine the mean-square values of random processes having the following spectral densities: a) 25x(w) b) Sx (2() c) Sx(w/2) 3. Consider a stationary random process with spectral density defined as: Sx(w) = 3216(w) + 876(w - 3) + 876(w + 3) + 32no(w -6) + 32no(w +6) a) What is the mean value of this process? b) What is the variance of this process? c) What are the discrete frequencies of this process