Supervised Learning with Convolutional Neural Networks (CNNs) is the optimal choice for image classification tasks like pedestrian detection. CNNs are designed for such tasks, while the other options are not suitable for image classification. Apriori is used for association rule mining, reinforcement learning for decision-making, and DBSCAN for clustering.

Apache Spark offers an optimized engine that supports real-time computations. This capability enables faster data analytics by allowing Spark to process data as it arrives, making it suitable for real-time data processing and analytics tasks. This is a key advantage of Spark over traditional batch processing systems.

The median is the middle value in a dataset when it's ordered. It's a measure of central tendency that's not affected by extreme values (outliers). To find the median, you arrange the data in ascending order, and if there's an even number of values, it's the average of the two middle values.

Hybrid recommender systems leverage both collaborative filtering (user-user/item-item) and content-based methods to provide more accurate recommendations. Collaborative filtering focuses on user behavior, while content-based filtering considers item attributes.

The T-test for independent samples is used to determine if there is a significant difference between the means of two independent groups. It is commonly employed in hypothesis testing to compare means. The chi-squared test is used for testing the independence of categorical variables, ANOVA for comparing more than two group means, and the correlation test for measuring the strength and direction of a linear relationship.

The Convolutional layer in Convolutional Neural Networks (CNNs) is responsible for detecting local features in the input data, such as edges and textures. It does this by applying convolution operations across the input data, which allows the network to recognize spatial patterns in images or other structured data.

Collaborative Filtering is a recommendation approach that identifies users similar to the target user based on their interactions and recommends items liked by those similar users. It relies on user-user similarity for recommendations.

Linear Regression is a commonly used algorithm for predicting continuous target variables. It establishes a linear relationship between the input features and the target variable, making it suitable for tasks like price prediction or trend analysis in Data Science.

In a data warehouse, the "Fact" table is used to store aggregated data at various levels of granularity. These tables contain measures or metrics, which are essential for analytical queries and business intelligence reporting.

Apache Flume is primarily used in the Hadoop ecosystem for data ingestion from various sources. It is a distributed, reliable, and available system for efficiently collecting, aggregating, and moving large amounts of data to Hadoop's storage or other processing components. Flume is essential for handling data ingestion pipelines in Hadoop environments.