(7分)若小貝打算用E(p|HHH)來推估p，則她的估計值為多少？      (13)

題組內容

2. 阿正手上展示一個有正反兩面不同花樣的鋼板(正面以H表示，反面以T表示)，令p代表隨機投擲一次會出現正面的機率。小飛與小貝欲估計p的值，並要求阿正給點提示。阿正於是擲投此鋼板三次得到三個正面，以HHH表示。
2.2 小貝是貝氏學派統計學家(Bayesian statistician)，她在還未看到阿正的樣本前其對 p認知的先驗機率分配(prior distribution)如下表所示：

二、請閱讀下列之摘錄文，並詳述其意涵及評論其內容。(25分)Rising rents, stagnant wages, and anemic housing production have led to generation high rent burden rates. Nearly 47 percent of renters across the country (USA) spend more than 30 percent of their household's total income on rent (Harvard Joint Center for Housing Studies 2020). As the crisis worsens and broad relief for renters is slow to materialize, many state and local governments are now considering whether to implement some variation of soft, second-generation rent regulations that limit rent increases (rent stabilization), as opposed to older, first-generation ones that mandate hard rent ceilings (rent control). Although rent regulations have been dismissed in some policy circles as costly ineffective, they have long been framed as affordability policies and viewed by renters as popular forms of public intervention. Based on our empirical analysis of rent savings and burden reduction for stabilized renters in New York City during the 1990s and 2000s, we argue that rent stabilization should be expanded and paired with policies that increase housing supply to provide a more robust response to the current housing affordability crisis.This research is especially important as the crisis expands and middle-income households become vulnerable populations that need protection against rent inflation. As politicians consider implementing new rent regulations to address growing affordability concerns, we provide evidence that rent stabilization reduces rents and promotes affordability in tight housing markets. Three research questions frame our work. First, who is most likely to benefit from rent stabilization? If higher income and more privileged renters predominately occupy rentstabilized units, that could undermine the ostensive equity objectives of such measures. While we view this critique as a red herring often used to suggest that rent regulation is a "bad" policy, we think it is sociologically important to know if policies thought to alleviate inequality could unintentionally exacerbate it. Second, how much rent, if any at all, do stabilization measures save tenants initially and over time? While it might be obvious that stabilized renters would save on rent compared to their non-stabilized counterparts, previous research suggests that stabilized tenants may pay a premium to gain access to stabilized units that will save them rent in the long run. Finally, doesstabilization reduce the share of rent-burdened households—that is, those spending more than 30 percent of their household income on housing costs? In light of our findings that rent stabilization can save tenants money and reduce rent-to-income ratios, we argue that it is an important policy tool that officials can leverage to address the ongoing affordability crisis.

題組內容

(7分)若小貝打算用E(p|HHH)來推估p，則她的估計值為多少？ (13)

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