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At all times, an urn contains N balls–some white balls and some black balls. At each stage, a coin having probability p, 0 < p < 1, of landing heads is flipped. If heads appears, then a ball is chosen at random from the urn and is replaced by a white ball. Let Xn denote the number of white balls in the urn after the nth stage.
(a)Is {Xn , n ≥ 0} a Markov chain? If so, explain why?(b) What are its classes? What are their periods? Are they transient or recurrent?(c) Compute the transition probabilities Pi,j .(d) Let N = 2. Find the proportion of time in each state.(e) Based on your answer in part (d) and your intuition, guess the answer for the limiting probability in the general case.(f) Prove your guess in part (c)(g) If p = 1, what is the expected time until there are only white balls in the urn if initially there are i white and N - i black?
The overall model statistically adequate at a 0.05 level of significance for predicting sale price(y)? For a moving average which is not true?
The probability that a house in an urban area will be burglarized is 5%. If 50 houses are randomly selected, what is the probability that one of the houses will be burglarized?
By using the normal distribution to approximate the desired probability.
The Pearson Product-Moment Correlation Coefficient (r) is a measure of linear relationship between two variables.
For the following data, determine whether or not right-hemisphere damage results in significantly reduced performance on the spatial skills task. Test with alpha set at .05 with one tail. The data are as follows:
When bucketing data for a histogram what is the standard way of dealing with data entries that are on the boundary of two buckets?
Could this information be viewed as representing the ratio scale of measurement? If so , explain why. If not, why not.
In a sample of 20 men, the mean height was 178 cm. In a sample of 30 women, the mean height was 164 cm. What was the mean height for both groups put together?
Faced with rising fax costs, a firm issued a guideline that transmissions of ten pages or more should be sent by two-day mail instead. Exceptions are allowed, but they want the average to be ten or below. Use Excel to find the right-tail p value
Find the best predicted temperature (in degree F) at a time when a cricket chirps 3000 times in one minute. What is wrong with this predicted value?
Suppose that the population follows the normal distribution. Forty trucks are randomly selected and weighed. Within what limits will 95 percent of the sample means occur?
The team wins 55% of their night games, and 85% of their day games. According to today's newspaper, they won yesterday. What is the probability the game was played at night?
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