1A. Check if numbers 1, 2, 3, 5, 4, 5 can represent lengths of a prefix code. Prove. 1B. The alphabet, and the symbol probabilities are provided below. Construct the Huffman code with a minimum variance. Show the tree construction, or use the algorithmic approach and write the list of codewords: Symbol Probability a1 0.1 a2 0.05 аз 0.05 a4 0.3 a5 0.4 a6 0.1
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- Joseph Bryan owns his own snow-cone business and lives 30 miles from a California beach resort. The sale of snow-cones is highly dependent on his location and on the weather. At the resort, his profit will be $120 per day in fair weather, $10 per day in bad weather. At home, his profit will be $70 in fair weather and $55 in bad weather. Assume that on any particular day, the weather service suggests a 40% chance of foul weather. Construct Joseph’s decision tree.Suppose that 60% of all students who have to buy a text for a particular course want a new copy, whereas the others want a used copy. Consider randomly selecting 15 purchasers, is a result of 12 a significantly high value for people who want a used copy of the book?One urn, U1, contains one blue ball (labeled B1) and three red balls (labeled R1, R2, and R3). A second urn, U2, contains two red balls (labeled R4 and R5) and two blue balls (labeled B2 and B3). An experiment is performed in which one of the two urns is chosen at random and then two balls are randomly chosen from it, one after the other without replacement. (a) Which of the following is a possibility tree that shows all possible outcomes of this experiment?
- Suppose that a study conducted by the Pew Research Center found the following: 38% of adults do not exercise regularly. 63% of the population is older than 44 years of age. 75% of the adult population is either aged 18–44 or exercises regularly. Find: a randomly selected adult exercises regularly. a randomly selected adult is aged 18–44. a randomly selected adult is 18–44 and exercises regularly. randomly selected 18-44 adult exercises regularly.Jaxon remembers that the passcode contains the digits 1, 2, 3 and 4, but he cannot recall their order. If Jaxon randomly enters these four digits, what is the chance that he will enter the correct code?According to scientists, the cockroach has had 300 million years to develop a resistance to destruction. In a study conducted by researchers, 6 comma 0006,000 roaches (the expected number in a roach-infested house) were released in the test kitchen. One week later, the kitchen was fumigated and 18 comma 10718,107 dead roaches were counted, a gain of 12 comma 10712,107 roaches for the 1-week period. Assume that none of the original roaches died during the 1-week period and that the standard deviation of x, the number of roaches produced per roach in a 1-week period, is 1.61.6. Use the number of roaches produced by the sample of 6 comma 0006,000 roaches to find a 9595% confidence interval for the mean number of roaches produced per week for each roach in a typical roach-infested house. Find a 95% confidence interval for the mean number of roaches produced per week for each roach in a typical roach-infested house.
- A fourth-grade teacher suspects that the time she administers a test, and what sort of snack her students have before the test, affects their performance. To test her theory, she assigns 90 fourth-grade students to one of three groups. One group gets candy (jelly beans) for their 9:55 AM snack. Another group gets a high-protein snack (cheese) for their 9:55 AM snack. The third group does not get a 9:55 AM snack. The teacher also randomly assigns 10 of the students in each snack group to take the test at three different times: 10:00 AM (right after snack), 11:00 AM (an hour after snack), and 12:00 PM (right before lunch). Examining the graph and the table of means, which of the following is a null hypothesis that might be rejected using a two-factor analysis of variance? Check all that apply. There is no interaction between the type of snack and the time of test μ10:00 AM10:00 AM ≠ μ11:00 AM11:00 AM ≠ μ12:00 PM12:00 PM μ10:00 AM10:00 AM = μ11:00 AM11:00 AM =…at a factory the emplyess were surveted and classified according to their level of education and if they smoked. educational level smoking habit Not hs graduate hs graduate college graduate smoke 6 14 19 dont smoke 18 7 25 if an emolyee is selected at random find these prob. a) the emplyoee smokes given that he or she graduated from college b) given that the employee did not graduate hs, he or she is a smokerPeople are classified as hypertensive if their systolic blood pressure (SBP) is higher than a specified level for their age group, according to the algorithm in the table below. Assume SBP is normally distributed with mean, and standard given in the table for age groups 1 – 14 and 15 – 44, respectively. Define a family as a group of two people in age group 1 – 14 and two people in age group 15 – 44. A family is classified as hypertensive if at least one adult and at least one child are hypertensive. i. What proportion of 1 – 14-year-olds are hypertensive? ii. What proportion of 15 – 44-year-olds are hypertensive?
- 1). Cognitive science consistently shows that one of the most effective studying tools is to self-test. A recent study reinforced this finding. In the study, 118 college students studied 48 pairs of Swahili and English words. All students had an initial study time and then three blocks of practice time. During the practice time, half the students studied the words by reading them side by side, while the other half gave themselves quizzes in which they were shown one word and had to recall its partner. Students were randomly assigned to the two groups, and total practice time was the same for both groups. On the final test one week later, the proportion of items correctly recalled was 15% for the reading-study group and 42% for the self-quiz group. The standard error for the difference in proportions is about 0.07. Test whether giving self-quizzes is more effective and show all details of the test. The sample size is large enough to use the normal distribution. 2). Using the…If 2% of a population has a genetic mutation and 100 people are randomly selected what is the mean for the number of people with the genetic mutation is such groups of 100?In an online poll run by a Hong Kong newspaper, 45% of people declared they go to the gym once a week, 25% go two times, 10% go three times, and the rest do not go. The data were collected through telephone interviews with 650 people; 230 answered they do not go to a gym at all, 150 go once a week, 200 go twice a week, and the rest go three times each week.a. Can this be considered to be a multinomial experiment? Which characteristics must it have to be classified as such?b. Would you use a goodness of fit test? Why?c. What conclusions would you gather from it? Do the online results match the phone interviews?d. If not, could you suggest any reasons why they are different?
