(2) Determine whether this estimator is unbiased. Justify your answer.(Hint: Let S = -Σi=1^n (Xi) Gamma(n, θ), and E(1/S) = θ/(n-1) if $n &gt; 1$.)

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2026/10/22

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II.1. The recruitment channels for a company are as follows: based on past experience, 50% of applicants learned of the openings through job banks, 10% through social media ads, 30% through employee referrals, and 10% through campus recruiting. The one-year turnover rates (the probability of an employee resigning within a year) are as follows: 10% for those from job banks, 20% for those from social media ads, 5% for those from employee referrals, and 30% for those from campus recruiting. If an employee is still with the company after one year, what is the probability that he (she) originally learned about the recruitment information through a job bank? (7%)

題組內容

(2) Determine whether this estimator is unbiased. Justify your answer.

(Hint: Let $S = -\sum{i=1}^n \ln(Xi) \sim \text{Gamma}(n, \theta)$, and $\operatorname{E}\left(\frac{1}{S}\right) = \frac{\theta}{n-1}$ if $n > 1$.)

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題組內容

(2) Determine whether this estimator is unbiased. Justify your answer.(Hint: Let $S = -\sum{i=1}^n \ln(Xi) \sim \text{Gamma}(n, \theta)$, and $\operatorname{E}\left(\frac{1}{S}\right) = \frac{\theta}{n-1}$ if $n > 1$.)

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相關試卷

(2) Determine whether this estimator is unbiased. Justify your answer.

(Hint: Let $S = -\sum{i=1}^n \ln(Xi) \sim \text{Gamma}(n, \theta)$, and $\operatorname{E}\left(\frac{1}{S}\right) = \frac{\theta}{n-1}$ if $n > 1$.)