I denna studie undersöks sambandet mellan ungdomars psykiska ohälsa, ofrivillig ensamhet och social isolering i ljuset av individens psykosociala miljö. Syftet är att utveckla en djupare förståelse för de dynamiska interaktionerna mellan dessa faktorer, och hur de bidrar till psykisk ohälsa och ökad ensamhet bland ungdomar. Vidare undersöker studien befintliga strategier och interventioner som kan hantera och minska ensamhet hos ungdomar, och deras effektivitet. Genom litteraturstudie belyser studien potentiella mekanismer bakom ensamhet hos ungdomar. Resultaten visar att ofrivillig ensamhet och/eller social isolering har en inverkan på psykisk hälsa och kan bidra till olika psykiska problem såsom depression och ångest. Det framkom att ingen enstaka variabel orsakar ensamhet, det är istället en mängd faktorer i individens psykosociala miljö som har inverkan. Ungdomar upplever olika typer av ensamhet, inklusive existentiell ensamhet, och uppfattningen av ensamhet är djupt subjektiv. Resultaten framhäver vikten av social inkludering/exkludering, familjens roll, kamratrelationers kvalitet samt betydelsen av mentorer, stödjande vuxna och professionella. Samtidigt lyfts bristen på specifika interventioner för att bekämpa ungdomars ensamhet. Trots detta påvisar studien att vissa interventioner, inklusive gruppbehandling, mindfulness och internetbaserade program, har positiva resultat. / This thesis aims to investigate the association between youths' mental health, involuntary loneliness, and social isolation, particularly focusing on the individual's psychosocial environment. Furthermore, this study examines existing strategies and interventions that can address and reduce loneliness among youths and the effectiveness of these interventions. Through a literature study of previous research, this study aims to deepen the understanding of the underlying mechanisms behind youths' loneliness. Findings demonstrate that involuntary loneliness and/or social isolation significantly impact mental health and can lead to various mental health disorders such as depression and anxiety. It is evident that there isn't a single variable causing loneliness, instead, several factors within the individual's psychosocial environment play a role. Youths’ experience different types of loneliness, including existential loneliness, and perceptions of loneliness are deeply subjective. The present thesis underscores the importance of social inclusion and exclusion, the role of the family, the quality of peer relations, and the significance of mentors, supportive adults, and professionals. It highlights the lack of specific interventions to combat loneliness among youths. Despite this, the study indicates that certain interventions, including group therapy, mindfulness, and internet-based programs, yield positive results.

In this paper, we first present the basic principles of set theory and combinatorial analysis which are the most useful tools in computing probabilities. Then, we show some important properties derived from axioms of probability. Conditional probabilities come into play not only when some partial information is available, but also as a tool to compute probabilities more easily, even when partial information is unavailable. Then, the concept of random variable and its some related properties are introduced. For univariate random variables, we introduce the basic properties of some common discrete and continuous distributions. The important properties of jointly distributed random variables are also considered. Some inequalities, the law of large numbers and the central limit theorem are discussed. Finally, we introduce additional topics the Poisson process.