5. Consider the problem of predicting how well a student does in her second year of college/university, given how well she did in her first year. Specifically, let x be equal to the number of "A" grades (including A-. A and A+ grades) that a student receives in their first year of college (freshmen year). We would like to predict the value of y, which we define as the number of "A" grades they get in their second year (sophomore year). Here each row is one training example. Recall that in linear regression, our hypothesis is he(x)=0o+O;x, and we use m to denote the number of training examples. y 4 3 4 1 4 3 For the training set given above, what is the value of m? (which should be a number between 0 and 10).

Sam is a competitive swimmer that competes in the 100 m freestyle and 100 m backstroke.  High school swimming state averages are as follows: Freestyle:  mean time 72.39 seconds, standard deviation 3.7 seconds Backstroke:  mean time 81.09 seconds, standard deviation 4.1 seconds   If Sam's times were 71.1 seconds in freestyle and 80.1 seconds in backstroke, select the correct words to describe how his times compare to each other. Since the z-score in freestyle is       ["", ""]  than the z-score in backstroke, his time in freestyle is       ["", ""]  when compared to the rest of the swimmers in that event.

Please help step to step with Program R (CS) with explanation and final code for understanding thank you.

In the following, f(x), g(x) and h(x) are all positive value real functions. (Note: Answer true if for any possible positive value real function f(x) g(x) and h(x), the statement is true. If a counter example of f, g, and h can make the statement false, then it is false.) If f(x) is O(g(x)), then 2f(x) belongs to O(g(x)) If f(x) is O(g(x)), g(x) is O(h(x)), then f(x) belongs to O(h(x)) If f(x) and g(x) are O(n^2), then f(x)+g(x) belongs to O(n^2) If f(x) and g(x) are O(n^2), then f(x)-g(x) belongs to O(n^2) If f(x) is O(g(x)), and g(x) is O(n), then f(x)+g(x) belongs to O(n) If f(x)/g(x) = 100 for all x > 1000, then f(x) belongs to O(g(x)) %3D If f(x) belongs to O(g(x)), then 2^f(x) belongs to O(2^g(x))

Hat-check problem. Use indicator random variables to solve the following problem, which is known as the hat-check problem. Each of n customers gives a hat to a hat-check person at a restaurant. The hat-check person gives the hats back to the customers in a random order. What is the expected number of customers who get back their own hat?

41 In most of Europe and Asia annual automobile insurance is determined by the bonus malus system. Each policyholder is givena number (state) and the policy premium is determined as a function of this state. A policy holder's state changes from year to year in response to the number of claims made by the policy holder. Suppose the number of dlaims made by a particular policyholder in any given year, is a Poisson random variable with parameter A. Let. sj(k) be the next state of a policyholder who was in state i in the previous year and who made k claims in that year. The following table is a simplified Bonus-Malus system having 4 states Next state if Annual Premium State O claims 1 claim 2 claims 3 or more claims 1 200 1 3 4 250 3 4 4 4. 4. 400 2 600 3 4 4 4. 4 For A=2 A. Find the mean time to retum to state 1 (if you start in state 1): (round to 2 decimals) (round to 2 B. Find the expected annual premium for a random person after it has been with the insurance company for a while:…

World Series odds Consider two teams, A and B, playing a series of games until one of the teams wins n games. Assume that the probability ofA winning a game is the same for each game and equal to p, and the probability of A losing a game is q = 1− p. (Hence, there are no ties.) Let P(i, j) be the probability of A winning the series if A needs i more games to win the series and B needs j more games to win the series. a. Set up a recurrence relation for P(i, j) that can be used by a dynamic programming algorithm. b. Find the probability of team A winning a seven-game series if the proba-bility of it winning a game is 0.4. c. Write pseudocode of the dynamic programming algorithm for solving this problem and determine its time and space efficiencies.