Problem_set_2 Sustainability Science 5060 Problem Set #2 – due October 16, 2020 Write Matlab code to solve the following problems. Submit your code and your answers. 1. Assume that the average January...

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Problem_set_2 Sustainability Science 5060 Problem Set #2 – due October 16, 2020 Write Matlab code to solve the following problems. Submit your code and your answers. 1. Assume that the average January temperature in NYC Central Park has a Gaussian distribution with mean µ = 33.3°F and standard deviation σ = 4.48°F. (a) How much more likely is it to observe this mean temperature (µ) than the temperature that was observed in January 2020 (39.1°F)? (b) The coldest January ever recorded occurred in 1918, when the average temperature was 21.7°F. What is the probability of observing a temperature this cold or colder? You should solve this problem using the equations for the Gaussian distribution presented in the lectures. You should not use the built-in Matlab functions normpdf and normcdf in your submitted code, although you can use these functions to verify your answers if you wish. Hint: for (b), use the built-in Matlab function erf to evaluate the error function. Also note that inf is a built-in Matlab constant referring to infinity. 2. A vector T stores the observed January temperature in Central Park for the last ten years (2011-2020), with T=[29.7 37.3 35.1 28.6 NaN 34.5 38.0 NaN 32.5 39.1]. We’ve assumed here that the data are missing for the years 2015 and 2018 (they’re not really), and have assigned a value of NaN (not a number) for these years. Write code that will do the following: (a) Identify missing values (NaNs) in the vector T, and store the associated indices in a new variable. Do this using the built-in Matlab functions find and isnan. (b) Print to the screen the indices associated with the missing values in T. (c) Using these indices, assign a temperature value to the missing years (i.e., modify the vector T), where this value is simply the arithmetic average of the temperature in the year before and the year after.