(a) (4%) Find a uniformly most powerful (UMP) test of size \( \alpha \in (0, \frac{1}{4}) \) for \( H_0: P = P_0 \) versus \( H_1: P = P_1 \), where \( P_0 \) is \( N(0,1) \) and \( P_1 \) is the double exponential distribution with the p.d.f. \( \frac{1}{4}e^{-|x|/2} \). [Hint: \( \int_{1}^{\infty} \frac{1}{\sqrt{2\pi}} e^{-x^2/2} dx \approx 0.1587 \)]

(b) (4%) Find the power function of the test in (a).

一、下面這一段來自犯罪學者 George Vold 的《理論犯罪學》，*Theoretical Criminology*，請做個理論說明與評論。(25 分) The Anomie Tradition The term anomie is derived from an ancient Greek word meaning “lawlessness.” In criminology it is important because of its use by Emile Durkheim and Robert K. Merton in their discussions on the structure of society and the effects that structure can have on individuals within society. These writers used “anomie” to designate a state of “normlessness” in society which could have the effect of generating deviant behavior in individuals. Like Lombroso, who had written his major work approximately 20 years earlier, Durkheim was reacting against the classical assumptions that man was free in a contractual society. But whereas Lombroso focused on the determinants of human behavior within the individual, Durkheim focused on society and its organization and development. Durkheim’s original formulation of anomie was later revised by Merton, who applied it directly to American society. In this form, it gained widespread acceptance, and subsequently provided the ideological underpinning for Lyndon Johnson’s War on Poverty.

二、下面這段論文來自 David Jones 的《犯罪學歷史》，History of Criminology，請做內容說明與評論。(25 分) In his 1970 book, *The Social Reality of Crime*, Richard Quinney went on to recite six conflict-oriented propositions concerning the nature and etiology of crime: 1. Crime is a definition of human conduct that is created by authorized agents in a politically organized society. 2. Criminal definitions describe behaviors that conflict with the interests of the segments of society that have the power to shape public policy. 3. Criminal definitions are applied by the segments of society that have the power to shape the enforcement and administration of criminal law. 4. Behavior patterns are structured in segmentally organized society in relation to criminal definitions and within this context persons engage in actions that have relative probabilities of being defined as criminal. 5. Conceptions of crime are constructed and diffused in the segments of society by various means of communication. 6. The social reality of crime is constructed by the formulation and application of criminal definitions, the development of behavior patterns related to criminal definitions, and the construction of criminal conceptions. 　Quinney drew upon several earlier criminological theories in formulating his six propositions. His first proposition, for instance, has origins in the pragmatic perspective of the "interactionists," particularly labeling theorists, while his second proposition stems in large measure from Vold, as does his third, and his fourth proposition comes from Sutherland's differential association theory. The last two of Quinney's propositions seem to flow at least partially from a 1966 book by sociologists Peter L. Berger and Thomas Luckmann, *The Social Construction of Reality*, wherein they observed the subjectivity of society and its dependency upon both individual perception and ideology.

三、請評論傳統犯罪學與刑法學中，以犯罪人為理性的假設，是否有可以再討論的空間？理由為何？ (25 分)

四、請分析我國監獄超收近 20%(容量 54,000 人，現收容約 64,000 人)背後的可能原因。 (25 分)

一、請問何謂質化研究(qualitative research)？試申論之。(30分)

二、請閱讀以下摘錄自〈全國國土計畫〉第三章「發展預測」(第12頁)內容後，自行決定研究主題，設計一份質化研究取徑的論文計畫書；計畫書內容至少包括研究題目、問題意識、研究目的、研究方法、研究流程、研究預期貢獻。(70分)

1. Calculus( 50%)。清楚完整作答始得完全分數。(1). Find the slant asymptotic(斜漸進線) for \( F(x, y) = x^3 + y^3 - 3xy = 0 \) (6%)

(2). If \( f_0(x) = \sqrt{x} \), and \( f_{n+1}(x) = \sqrt{2 + f_n(x)} \). Find the limit \( \lim_{x \to 4} \frac{f_2(x) - 2}{x - 4} = ? \) (6%)

(3). Find the limit \( \lim_{x\to 0}\frac{\cos(\sin x) + \sin(1 - \cos x) - 1}{x^2} = ? \) (6%)

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