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- The price of a stock is modeled with a geometric Brownian motion with drift μ=-0.25 and volatility σ=0.4. The stock currently sells for $35. What is the probability that the price will be at least $40 in 1 year?Consider a simple model of the hunting behaviour of a fox. In a single day, the fox catches either 0 or 1 rabbits, with probabilities 0.3 and 0.7, respectively. The outcome of hunting on day m is independent of all other days.We describe this system through a discrete-time, discrete-state stochastic process R(m), where R is the total number of rabbits caught between the end of day 0 (defining a starting point of our observation) and the end of day m. m = 0,1,2,3... is thus a discrete time parameter, and R(0) = 0 by definition (a) It can be shown that pr(m) – the probability of catching R = r rabbits in m days – is given by a binomial distribution (see Appendix A.2.1). Here, m is the number of “trials”, r the number of successes and q = 0.7 the probability of success. Hence give expressions for:i The mean number of rabbits caught after m days. ii The standard deviation of the total number rabbits caught after m days. iii The standard deviation of the mean number of rabbits caught per day…8 Prove the ergodic-stochastic transformation.
- Explain the nature of and the difficulties caused by each of the following: a. Heteroscedasticity b. Autocorrelated errors[stochastic process1]1. A researcher observed a rat respond for a food reward by pressing one of the three levers in a cage. Pressing the lever to the right (R) produced no food reward. pressing the lever to the left (L) produced a single food pellet, and pressing the lever at the center (C) produced two food pellets. Because the center level produced the largest reward, the researcher hypothesized that the rat would press this lever most often. Each trial ended when the rat produced a level. The researcher recorded lever pressing for 30 trials. L, L, R, L, R, C, R, L, C, L, L, C, C, C, R, C, R, C, L, C, C, L, C, C, C, L, C, C, C, C, C - Create the appropiate graph for this data - Do these data support the hypothesis? Explain. 2. Which scales of measurement are assumed to be discrete? What does this mean? Which scales of measurement are assumed to be continuous? What does this mean? 3. What type of graph should you create to visualize the following frequency data? Explain. -…