The Following Questions are of the course"Mathematical Analysis For Computer Science".Please Do not use any kind of AI tools such as Chatgpt,Bard,AI Bing while providing the answer.***If you use AI tools I will downvote you and submit a negative comment against you as Chatgpt or Bard gives wrong answers all the time.I need human generated answers.If you are unable to solve by your own,skip it.Thanks In Advance
Question No 01
Suppose. a circular pizza is being divided into pieces by straight cuts and Ln represents the maximum number of slices obtained from the pizza by n straight cuts. Formulate the recurrence relation on Ln and find its closed form expression for each of the following cases. i. When each straight cut passes through the center of the pizza What each straight cut is parallel to the previous cuts through the pizza jii. When none of the straight cuts are parallel to cach-other and none of them go through any of the previous intersection points
Question No.02
Cross fertilizing a Red and a White flower produces White flowers 60% of the time. Now we cross fertilize five pairs of Red and White flowers and produce five offspring. Find the probability that there will be majority of Red flowered plants in the five offspring. Also mention the names of two different random variables which have the memoryless property
Question No.03
Suppose that, whether the Bangladesh cricket team wins today depends on their performance through the last two days. If they have won in the past two days, then they will win the next match with probability 0.8.If they have won today but not yesterday,then they will win tomorrow with probability O.6.If they have won yesterday but not today,then they will win tomorrow with probability 0.2. If they have not won in the past two days, then they will not win tomorrow with probability 0.7. i) What is the probability that they will win on Thursday,but not on Friday given that they already won on both Monday and Tuesday? ii) What is the probability that they will not win on Friday,given that they won neither on Monday nor on Tuesday?