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Claude Aifoundations — practice by topic

Browse 95 questions across 8 Aifoundations topics. Choose what you want to revise, then open a question to check its answer and worked solution.

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Aifoundations topics

AlexNet CNN ImageNet (16)Many Shot in Context Learning (14)Linear Regression and Supervised Learning (13)Math for AI LA Probability (13)InstructGPT RLHF (11)MLP and Activations (10)Transformer Attention (9)What Is AI Intro (9)

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A probability mass function (PMF) for a DISCRETE random variable X has the propertyRead the answer and worked solution →The expectation of a Bernoulli(p) random variable isRead the answer and worked solution →Given matrices A ∈ ℝ^(m×n) and B ∈ ℝ^(n×p), the product AB exists and lies inRead the answer and worked solution →The variance of a random variable X is defined asRead the answer and worked solution →

Worked practice questions

A probability mass function (PMF) for a DISCRETE random variable X has the property

  1. Σ p_X(x) over Val(X) equals 0
  2. p_X(x) can exceed 1 for some x
  3. p_X(x) is undefined at x = 0
  4. Σ p_X(x) over Val(X) equals 1
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Correct answer: D. Σ p_X(x) over Val(X) equals 1

A PMF satisfies 0 ≤ p_X(x) ≤ 1 and Σ p_X(x) = 1 over all values X can take. PDFs (continuous case) can exceed 1 in value but their INTEGRAL is 1 this is a common confusion.

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The expectation of a Bernoulli(p) random variable is

  1. p(1 − p)
  2. 0
  3. p
  4. 1 − p
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Correct answer: C. p

X ~ Bernoulli(p) takes value 1 with probability p and 0 with probability 1 − p. E[X] = 1·p + 0·(1 − p) = p. Variance is p(1 − p).

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Given matrices A ∈ ℝ^(m×n) and B ∈ ℝ^(n×p), the product AB exists and lies in

  1. ℝ^(m×p)
  2. ℝ^(m×n)
  3. ℝ^(n×p)
  4. ℝ^(p×m)
Show answer and solution

Correct answer: A. ℝ^(m×p)

Matrix multiplication requires inner dimensions to match (n = n) and produces a matrix with the outer dimensions: m rows × p columns.

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