Apr 5, 2018 · Two people decided to play a coin toss game. The rules of the game are: (i) Everyone plays 2 times in sequence; (ii) the first to obtain two head wins; Suppose that the two individuals names are...

The problem can be mapped on a one-dimensional discrete random walk. Imagine that you start at 0 and you make a step +1 (for the outcome HT) with probability 1 / 4, a step -1 (for the outcome TH) with probability 1 / 4, and a step 0 (for the outcomes TT and HH) with probability 1 / 2. The question about the number of coin tosses after which both have accumulate the same number of heads is then ...

Jan 15, 2018 · We toss n = 200 n = 200 Euro coins on the table. I want to calculate, using the central limit theorem, the probability that at least 110 110 coins have tutned on the same side.

Jan 9, 2019 · Given a coin with an unknown bias and the observation of N N heads and 0 0 tails, what is expected probability that the next flip is a head? i want to solve with MLE, not Bayesian analysis. My attempt: For any value of p , the probability of k Heads in n tosses is given by (n k)pk(1 − p)n−k (n k) p k (1 − p) n − k Consider the maximization problem: ∂pk(n k)(1−p)n−k ∂p = …

Oct 24, 2023 · Goal: Participate in a coin-tossing game with the aim to maximize your earnings. A fundamental part of the game is formulating a strategy that optimizes your earnings based on the observation of th...

Dec 9, 2016 · A coin tossed 10 times. what is the probability that the coin lands on 'Heads' less than 'Tails' given that the first toss was 'Heads'? Say X indicating how many times the coin landed on Heads Y

Jan 22, 2019 · There is some misunderstanding in your model, because you mixed up one single toss with the whole experiment. The right model: You have n n random variables Xi, i = 1, …, n X i, i = 1, …, n which are identically and independently distributed.

May 24, 2024 · In one of his interviews, Clip Link, Neil DeGrasse Tyson discusses a coin toss experiment. It goes something like this: Line up 1000 people, each given a coin, to be flipped simultaneously Ask eac...

Jul 13, 2018 · Note that for countable Ω Ω it is perfectly reasonable to take power set as sigma algebra, but once it’s uncountable, we can’t because it gets too large. This is what Borel showed if you are interested in further details. Hence, we consider the smallest sigma algebra, usually generated by a collection of sets of interest.

Oct 14, 2017 · Assume that you choose point $\\xi$ from $[1,4]$ in the following way. You toss a coin that can give head, tail or stood on edge with equal probabilities. If it stood on edge, then $\\xi = 3$. If tail,