Start learning →

Claude Math for AI LA Probability — practice questions

Explore 13 free Math for AI LA Probability questions in Claude Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

Practise Math for AI LA Probability with Quill →

Math for AI LA Probability questions and exercises with answers

Showing questions 1–13 of 13.

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 →The trace of a matrix A ∈ ℝ^(n×n), tr(A), isRead the answer and worked solution →For two independent random variables X and YRead the answer and worked solution →A Binomial(n, p) random variable has mean and varianceRead the answer and worked solution →A matrix A is INVERTIBLE if and only ifRead the answer and worked solution →Bayes's rule allows you to computeRead the answer and worked solution →For the standard NORMAL distribution N(0, 1), the mean and variance areRead the answer and worked solution →Eigenvalues λ of a square matrix A satisfyRead the answer and worked solution →For a Poisson(λ) random variable, the mean equals the variance and both equalRead the answer and worked solution →Conditional probability 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
Show answer and solution

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.

Open this question →

The expectation of a Bernoulli(p) random variable is

  1. p(1 − p)
  2. 0
  3. p
  4. 1 − p
Show answer and solution

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).

Open this question →

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.

Open this question →

How to practise

  1. Choose a Math for AI LA Probability question and try to work out your answer.
  2. Open the question to check the correct answer and read its worked solution.
  3. Continue in the app for bite-sized lessons, explanations and review with Quill. You can start without creating an account.