2. Let X1, , Xn be i.i.d. random variables with probability density function f(x; θ) = θ x^θ - 1, 0 < x < 1, θ > 0. (10%) (1) Derive the maximum likelihood estimator (MLE) of θ

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%)

2. Let $X1, \ldots, Xn$ be i.i.d. random variables with probability density function $f(x; \theta) = \theta x^{\theta - 1}, 0 < x < 1, \theta > 0$. (10%)

(1) Derive the maximum likelihood estimator (MLE) of \(\theta\)

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2. Let $X1, \ldots, Xn$ be i.i.d. random variables with probability density function $f(x; \theta) = \theta x^{\theta - 1}, 0 < x < 1, \theta > 0$. (10%) (1) Derive the maximum likelihood estimator (MLE) of \(\theta\)

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相關試卷

2. Let $X1, \ldots, Xn$ be i.i.d. random variables with probability density function $f(x; \theta) = \theta x^{\theta - 1}, 0 < x < 1, \theta > 0$. (10%)

(1) Derive the maximum likelihood estimator (MLE) of \(\theta\)