In an era marked by globalization, proficiency in foreign languages has become increasingly vital for success in various fields. Higher education institutions play a crucial role in equipping students with these skills. However, teaching foreign languages involves more than merely imparting vocabulary and grammar; it requires fostering cognitive engagement to facilitate deeper understanding and retention.

In this article, we will explore the basic concepts of the Markov chain, its relation to the Bernoulli scheme, and the transition matrix. We will also consider the importance of this theory in social life.

Mazkur maqolada O‘zbekiston Respublikasi Tiklanish va taraqqiyot jamg‘armasi faoliyatining tashkil etilish zarurligi tahlil qilinadi. Jamg‘armaning iqtisodiy rivojlanish jarayonida tutgan o‘rni, uning mamlakatning ijtimoiy va iqtisodiy taraqqiyotiga qo‘shgan hissasi, shuningdek, innovatsiyalarni joriy etish va yangi investitsiyalarni jalb qilishdagi roli haqida fikrlar bildiriladi. Maqola O‘zbekiston iqtisodiyotining barqaror rivojlanishini ta’minlash va raqobatbardoshligini oshirish maqsadida jamg‘armaning asosiy vazifalarini ochib beradi.

This article discusses the role of the left eardrums in the singer's breathing, the weight of the sound apparatus, and how to practice breathing.

This article provides an in-depth analysis of various directions for the development of stock market trading systems. Modern technologies, in particular, innovative solutions such as electronic trading systems, blockchain technology and artificial intelligence are introduced as one of the main factors of the stock market, which play an important role in making trading processes fast, transparent and secure. Electronic trading platforms enable traders to execute transactions in real time, thereby increasing market liquidity. The introduction of blockchain technology into the stock market will make trading transactions a more reliable and traceable system. With the help of this technology, the security of transactions and their transparency increases, which increases the confidence of market participants. Also, artificial intelligence and algorithmic trading will expand the possibilities of analytical and strategic decision-making in the stock market, which will create new opportunities for investors to trade more effectively. The need for integration with international trade systems is of great importance in the process of development of Uzbekistan's stock market. Through this integration, local companies will have the opportunity to participate at the international level, which will increase the global competitiveness of the stock market of Uzbekistan. Also, by adapting international experiences to local conditions, the efficiency of the stock market can be increased.