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Principal component analysis ( PCA) is a linear dimensionality reduction technique with applications in exploratory data analysis, visualization and data preprocessing . The data is linearly transformed onto a new coordinate system such that the directions (principal components) capturing the largest variation in the data can be easily identified.
Find $P(A|C), P(B|C), P(A \cap B|C), P(A), P(B),$ and $P(A \cap B)$. Note that $A$ and $B$ are NOT independent, but they are conditionally independent given $C$.
When an event is described to you as something that could possibly happen, the complement of that event is every other possible thing that could happen. There is a box with red, blue, and green balls. A ball is drawn at random from the box. Let R R be the event that a red ball is drawn. Describe R^c Rc.
Given a randomly chosen bag triggers the alarm, what is the probability that it contains a forbidden item? Let's break up this problem into smaller parts and solve it step-by-step. Starting a tree diagram.
When A and B are independent, P(A and B) = P(A) * P(B); but when A and B are dependent, things get a little complicated, and the formula (also known as Bayes Rule) is P(A and B) = P(A | B) * P(B).
- 7 min
- Sal Khan
If $C$ is the event that it is cloudy, then we write this as $P(R | C)$, the conditional probability of $R$ given that $C$ has occurred. It is reasonable to assume that in this example, $P(R | C)$ should be larger than the original $P(R)$, which is called the prior probability of $R$.
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