3. (а) What is the probability that a 5-card poker hand has at least three spades? (b) this probability? What upper bound does Markov's Theorem give for (c) for this probability? What upper bound does Chebyshev's Theorem give
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- Based on the data that has been gathered what is the probability of disasters in July & Augustus using Markov chain ?Q2) In a language school, the path of a student's language level has been modeled as a Markov Chain with the following transition probabilities from the lowest level (Beginner) through the highest level (Advanced): Beginner Elementary Intermediate English Upper-Intermediate Quit Advanced Beginner Elementary Intermediate English Upper-Intermediate 0.4 0.1 0.05 0.45 0.1 0.5 0.3 0.1 0.1 0.4 0.3 0.2 0.2 0.4 0.2 0.2 Quit 1 Advanced Each student's state is observed at the beginning of each semester. For instance; if a student's language level is elementary at the beginning of the semester, there is an 30% chance that she will progress to intermediate level at the beginning of next semester, a 50% chance that she will still be in the elementary level, a 10% chance that she will regress to beginner level and 10% chance that she will quit the language school. Find the probability that a student with beginner level will eventually have an advanced level. Assume beginner level is state 1,…Suppose I flip n independent biased coins such that the jth coin has probability j/n of being heads, for j = 1,...,n. Let Hn be a random variable equal to the total number of heads. (a) What is the expectation of H,? (b) What is the variance of Hn? (c) Use Markov's inequality to derive an upper bound on P(Hn 2 9n/10).
- Don't copy Chegg give new answer ASAP3.2: Markov Chains are Proper Probabilistic Models Show that the sum of the probabilities over all possible sequences of any length is 1. This proves that the Markov chain describes a proper probability distribution over the whole space of sequences.A study of armed robbers yielded the approximate transition probability matrix shown below. The matrix gives the probability that a robber currents free, on probation, or in jail would, over a period of a year, make a transition to one of the states. То From Free Probation Jail Free 0.7 0.2 0.1 Probation 0.3 0.5 0.2 Jail 0.0 0.1 0.9 Assuming that transitions are recorded at the end of each one-year period: i) For a robber who is now free, what is the expected number of years before going to jail? ii) What proportion of time can a robber expect to spend in jail? [Note: You may consider maximum four transitions as equivalent to that of steady state if you like.]
- Exercise 49 Let X NegBinom(900, ). Estimate the probability P(X > 3000) (i) with the Markov inequality, (ii) with the normal distribution. Hint: Use the fact that a negative binomial random variable can be written as a sum of geometric random variables.A coffee shop has two coffee machines, and only one coffee machine is in operation at any given time. A coffee machine may break down on any given day with probability 0.2 and it is impossible that both coffee machines break down on the same day. There is a repair store close to this coffee shop and it takes 2 days to fix the coffee machine completely. This repair store can only handle one broken coffee machine at a time. Define your own Markov chain and use it to compute the proportion of time in the long run that there is no coffee machine in operation in the coffee shop at the end of the day.4