2.病毒行銷可能會面臨哪些挑戰與風險？企業應如何有效控管這些風險，在保護品牌形象的同時達到病毒行銷的目的？

五、深度偽造技術(Deepfake)在當代行銷領域中的應用以及所面臨的挑戰是什麼？請探討深度偽造技術對行銷策略的影響，分析其可能產生的風險和倫理問題。此外，企業應如何妥善利用此技術以增強廣告效果，同時避免對品牌信譽造成不良影響？(15%)

a. (7%) What is the probability that a 55-year-old, disease-free male will develop colon cancer over the next 5 years?

b. (8%) Suppose there is a cohort of 1000 50-year-old men who have never had cancer. How many colon cancers would be expected to develop in this cohort over a 15-year period?

a. (7%) If the binomial distribution holds, what is the probability distribution of the number of affected people in rooms with 2 occupants? That is, what is the probability of finding zero affected people? One affected person? Two affected people?

b. (10%) One useful summary measure of geographical clustering is the number of rooms with 2 or more affected occupants. If the binomial distribution holds, what is the expected number of rooms with 2 or more affected occupants over the entire nursing home?

c. (3%) Compare the observed number of rooms with 2 or more affected occupants with the expected number of rooms. Does this comparison give any evidence that clustering of disease occurs within rooms?Table 2Number of affected people and total number of people in a room for an outbreak of acute gastroenteritis in a nursing home in Baltimore, Maryland| People in room | Total number of rooms | Number of rooms with | | | | || --- | --- | --- | --- | --- | --- | --- || | | 0 affected people | 1 affected person | 2 affected people | 3 affected people | 4 affected people || 2 | 13 | 5 | 4 | 4 | 0 | 0 || 3 | 4 | 1 | 2 | 0 | 1 | 0 || 4 | 15 | 2 | 4 | 3 | 5 | 1 |

a. (10%) If the probability density function of the random variable \( X \) is \( f(x) \), find \( P(X < t) \) for all possible values of \( t \).

b. (5%) For all possible values of \( t \), find \( P(|X| < t) \).

a. (5%) If 9 students are taken as a simple random sample, what is the probability that the mean score will be between 67 and 71.5 points?

b. (5%) How many students must be selected so that the margin of error for the \( 95\% \) confidence interval of the mean score is within 5 points?

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