Consider a maximization problem that is being solved by Simulated Annealing. Let the objective function value of the current state, s, be 1000. Let this state have 5 successors/neighbors: s1(950), s2(975), s3(1000), s4(1000), and s5(1050). The numbers in parentheses represent the corresponding objective function values. The current temperature is 100. The probability that the next state is: 1. s1 = [Select] 2. s2 = [Select] 3. s3 [Select] = 4. s4= [Select] [Select] 5. s5 0.778 0.121 0.156 0.2 0.606

You decide to collect a bunch of cans of soda and measure the volume of soda in each can. Let the number of mL of soda in each can. Does qualify for being a random variable? Is it continuous or discrete? You want to study the efficiency of a machine producing nails over a day that is the number of faultless nails produced during the day. Assuming that the probability that a nail is produced is faultless is independent of the previous nail produced.  What is the random variable in this case? This random variable is __________(random/continuous)

(Please Solve problem by using your hand calculation and R). Suppose that X is the downloading time a movie, which follows a uniform distribution between 16 and 22 minutes. Let’s assume you want to download a movie. What is the probability that the download time will be (a) Less than 19 minutes? (b) More than 23 minutes? (c) Between 20 and 22 minutes? (d) What are the mean and standard deviation of the download times?

Different kinds of plants live on a planet. If the nutrient of a plant runs out (its nutrient level becomes zero), the plant wastes away. There are three kinds of radiation on the planet: alpha, delta, no radiation. The different species of plants react to radiation differently. The reaction involves a change in the nutrient level of the plant and the radiation the next day. The radiation of the next day will be alpha radiation if the sum of the demand for alpha radiation over all plants is greater than the sum of the demand for delta radiation by at least three. If the demand for delta radiation is greater by at least three than the demand for alpha radiation, the radiation will be delta. If the difference is less than three, there will be no radiation. There is no radiation the first day. Each plant has a name (string), a nutrient level (int), and a boolean that denotes whether it's alive. The plant species are wombleroot, wittentoot and woreroot. The different plant species react to…