# Probability and Statistics

## 2. Consider the Bloom filter discussed in Section 3.3. Define k = number of hash functions; N=number of bits in hash table; and D = number of words in dictionary. a. Show that the expected number of bits in the hash table that are equal to zero is expressed as * = (*) b. Show that the probability that an input word, not in the dictionary, will be falsely accepted as being in the dictionary is P = (1-0) c. Show that the preceding expression can be approximated as P = (1 – e *DIN)

EXPERT ANSWER The objective of this question is to test the student’s understanding of Bloom filters and their applications in computer science. Specifically, the question requires the student to derive three different expressions related to Bloom filters: the expected number of zero bits in the hash table, the probability of false positives, and an approximation …

## 8-56. Of 1000 randomly selected cases of lung cancer, 823

8-56. Of 1000 randomly selected cases of lung cancer, 823 resulted in death within 10 years. (a) Calculate a 95% two-sided confidence interval on the death rate from lung cancer. (b) Using the point estimate of p obtained from the preliminary sample, what sample size is needed to be 95% confident that the error in estimating the true …

## 7. Information supplied by a mail-order business for 12 cities is shown in Table P-7.

7. Information supplied by a mail-order business for 12 cities is shown in Table P-7. a. Determine the fitted regression line. b. Calculate the standard error of the estimate. c. Determine the ANOVA table. d. What percentage of the variation in mail orders is explained by the number of catalogs distributed? e. Test to determine …

## 8. In Bangladesh, 40% of male smokers smoke cigars. In a randomly selected sample of 20 male smokers, what is the probability that a. (2 mark) exactly 4 of the men smoke cigars? b. (2 marks) at most 3 of the men smoke cigars? c. (2 marks) at least 2 of the men smoke cigars? d. (3 marks) What are the expected value, variance, and standard Deviation of the above random variable?

EXPERT ANSWER Binomial distribution is used when the number of observations n is fixed, each observation is independent and also Each observation has two outcomes either success (p) or failure (q) and the probability of success p is the same for each outcome. Binomial distribution is used when the number of observations n is fixed, …

## a. Employ numerical summary measures to characterize the changes in homeownership rates across the country during this period. b. Do the trends appear to be uniform across the U.S. or are they unique to certain regions of

The file P02_51.xlsx contains data on U.S. homeownership rates. a. Employ numerical summary measures to characterize the changes in homeownership rates across the country during this period. b. Do the trends appear to be uniform across the U.S. or are they unique to certain regions of the country? Explain. EXPERT ANSWER a. Considering the problem containing …

## each sample of water has a 10% chance of containing a particular organic pollutant. assume that the samples are independent with regard to the presence of the pollutant. Find the probability that in the next 18 samples, exactly 2 contains the pollutant. (a) P(x

each sample of water has a 10% chance of containing a particular organic pollutant. assume that the samples are independent with regard to the presence of the pollutant. Find the probability that in the next 18 samples, exactly 2 contains the pollutant. (a) P(x 4) (b) P(x 4) (c) P(3 x 7) EXPERT ANSWER

## CBSSports.com developed the Total Player Ratings system to rate players in the National Basketball Association (NBA) based upon various offensive and defensive statistics. The following data show the average number of points scored per game (PPG) for 50 players with the highest ratings for a portion of the 2012–2013 NBA season. (CBSSports.com website, February 25, 2013).

CBSSports.com developed the Total Player Ratings system to rate players in the National Basketball Association (NBA) based upon various offensive and defensive statistics. The following data show the average number of points scored per game (PPG) for 50 players with the highest ratings for a portion of the 2012–2013 NBA season. (CBSSports.com website, February 25, …