The question is:
Continue the application of Bayes’ rule to compute the probability that a manager is a star after observing two years of “high” returns.?
the Answer is:
Consider the three scenarios: (High, High), (High, Low) and (Low, Low). We are interested in Pr (Star|High, High) using Bayes’ rule, this is equal to Pr(High, High兩 Star)Pr(Star) Pr(High, High)
.
Stars produce high returns in 20% of years, and so Pr(High, High兩 Star) = 20% * 20% Pr (Star) is still 10%. Finally, we need to compute Pr (High, High), which is
Pr(High, High兩 Star) Pr(Star) + Pr(High, High兩Normal) Pr(Normal). This value is 20% * 20% * 10% + 5% * 5% = 90% = 0.625%. Combining these values, 20% * 20% * 10% 0.625%
= 64%. This is a large increase from the 30% chance after one year.
Where does the "90%" come from in the sentence "This value is 20% * 20% * 10% + 5% * 5% = 90% = 0.625%" ?
Continue the application of Bayes’ rule to compute the probability that a manager is a star after observing two years of “high” returns.?
the Answer is:
Consider the three scenarios: (High, High), (High, Low) and (Low, Low). We are interested in Pr (Star|High, High) using Bayes’ rule, this is equal to Pr(High, High兩 Star)Pr(Star) Pr(High, High)
.
Stars produce high returns in 20% of years, and so Pr(High, High兩 Star) = 20% * 20% Pr (Star) is still 10%. Finally, we need to compute Pr (High, High), which is
Pr(High, High兩 Star) Pr(Star) + Pr(High, High兩Normal) Pr(Normal). This value is 20% * 20% * 10% + 5% * 5% = 90% = 0.625%. Combining these values, 20% * 20% * 10% 0.625%
= 64%. This is a large increase from the 30% chance after one year.
Where does the "90%" come from in the sentence "This value is 20% * 20% * 10% + 5% * 5% = 90% = 0.625%" ?
