dexy3222 dexy3222

24-05-2023
Mathematics

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On a quiet night, Jason was wandering in the campus. For each step, he would either move forward or backward. Further, we know that the probability that he moves forwards is 0 6 and the probability that he moves backward is 04. Define his initial coordinate as 0 and his coordinate will increase by if he moves one step forward and would be decreased by if he moves one step backward. After moving 10 times. a. Define X as the number of times that Jason moves forward, what distribution does X follow and what is the mean and variance?
b. Define Y as the coordinate, Jason after moving 10 times, is there a deterministic (ie, non-random) relationship between X and Y? If "yes", please write down the relationship and state why if your answer is "no"
c. What is the expected coordinate of Jason? What is the variance of Jason's expected coordinate?
d. What is the probability that Jason is located at the coordinate of 4

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