4. This question is about discrete probability. You are given a simple Bayesian network with two nodes as shown below. It represents a causal relationship between two variables for an advertising campaign on TikTok. ? P(X=x) T 0.1 Y x F 0.9 x ? P(Y=yl X=x) F 0.9 F F T 0.1 T F 0.25 T T 0.75 TikTok is a well-known and popular online short media clip platform. Companies can place adverts in TikTok that, when clicked, take the viewer to a particular TikTok company page. A company has decided to run an advertising campaign with a single advert leading to their company page. The advert does not always appear in a user stream during a session there is an algorithm that determines this. Sometimes when the advert appears, a user clicks on it and it taken to the company page. Sometimes a user just ignores the advert. However, the advert is not the only way the company page can be arrived at - there are links from other places around the web. The company wishes to analyse the effectiveness of their advertising campaign. The probability that the TikTok advert appear in someone's feed during a typical period is represented by the variable X, and the probability that someone visits the company page in a typical period is represented by the variable Y. a) Based on the available data, what is the probability that a user arrives at the company page during a typical period? [4 marks] b) The company notes that a new user has just arrived on their page. What is the probability that it was the advert that led to the user arriving on their page? [4 marks] c) Based on the data, for 5000 users in a typical period, how many visits to the company page would we expect all together (from advertising and other sources)? And how many of these visits could we attribute to the advertising? [2 marks] 4. This question is about discrete probability. You are given a simple Bayesian network with two nodes as shown below. It represents a causal relationship between two variables for an advertising campaign on TikTok. ? P(X=x) T 0.1 Y x F 0.9 x ? P(Y=yl X=x) F 0.9 F F T 0.1 T F 0.25 T T 0.75 TikTok is a well-known and popular online short media clip platform. Companies can place adverts in TikTok that, when clicked, take the viewer to a particular TikTok company page. A company has decided to run an advertising campaign with a single advert leading to their company page. The advert does not always appear in a user stream during a session there is an algorithm that determines this. Sometimes when the advert appears, a user clicks on it and it taken to the company page. Sometimes a user just ignores the advert. However, the advert is not the only way the company page can be arrived at - there are links from other places around the web. The company wishes to analyse the effectiveness of their advertising campaign. The probability that the TikTok advert appear in someone's feed during a typical period is represented by the variable X, and the probability that someone visits the company page in a typical period is represented by the variable Y. a) Based on the available data, what is the probability that a user arrives at the company page during a typical period? [4 marks] b) The company notes that a new user has just arrived on their page. What is the probability that it was the advert that led to the user arriving on their page? [4 marks] c) Based on the data, for 5000 users in a typical period, how many visits to the company page would we expect all together (from advertising and other sources)? And how many of these visits could we attribute to the advertising? [2 marks]