Mathematics homework help
Mathematics homework help. need help for both question 1 and 2. Please help. Thanks!1. (10 points) (Without Python) Your professors parents give her a $15 birthday present! Shehas a brilliant idea: ?y to Las Vegas and try to triple her money. In Vegas, your professorbegins with $15 and plays a game where the chance of winning each round is 49%. She eitherwins or loses $1 on each round. The game stops when she reaches $45 or goes bust. Let (Xn);’,°:0 be a SDTMC where X represents the your professors winnings at round n. (a) Find the transition probabilities for the Markov chain (Xn 20:0. (b) Calculate the probability that your professor will be ruined. That is, what is the proba-bility that she ends up with $0. (If youd like, you may show all of your work setting upa system of equations and then use Python to solve the system. If you choose to do so,please put your code in the .py ?le.) (c) Calculate the probability that the gambler will reach $45. (If youd like, you may show allof your work setting up a system of equations and then use Python to solve the system.Again, put your work in the .py ?le.) 2. (30 points) (With Python) In this Python exercise, you will compute the probability that yourprofessor goes to ruin and loses all her money. Be sure to annotate your code with shortexplanations of what you are doing (worth 10 points). Suppose (as above) that your professor starts with $15 and begins playing the betting game. (a) Simulate the gamblers ruin problem for your professor who starts with $15 and quits whenshe reaches $45 or goes bust. Use your code to simulate the probability of eventual ruin.Be sure to print your results. For example, print(The probability that my professor eventually loses all ofher money is %.3f. %probDfRuin) Start by simulating 500 sample paths of the Markov chain (Xn),3°=0. Find the probabilitythat your professor loses all of her money. (b) Using the simulated sample paths in part (a), compute the probability that your professorreaches $45. Print your results as in part (a). (G) Take a screenshot showing your code and your results together (e.g. side by side).
