Statistics
Probability I
Train on Probability I with 304 published problems. Preview a problem, explore the course outline, and work through one problem at a time.
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Preview a course problem
See a problem from Probability I before you begin.
Course topics
Course topics
Probability spaces, axioms, and rigorous counting
Conditional probability and independence
Random variables and distribution functions
Expectation, moments, and transforms
Joint distributions and conditional expectation
Modes of convergence, laws of large numbers, and CLT
Practice problems
Try a few Probability I problems, each with a hint.
- A spinner has four equally likely sectors, labelled A₁,A₂,B,C Free with an accountProbability spaces, axioms, and rigorous counting
- Choose a three-element subset uniformly from {1,…,9}, and let M be its largest element Free with an accountProbability spaces, axioms, and rigorous counting
- Roll two fair six-sided dice independently and record the ordered pair Conditional probability and independence
- Independent rounds of a game have three possible results: win with probability 2/7… Conditional probability and independence
- Roll two fair six-sided dice independently and let X be the absolute difference between… Random variables and distribution functions
- Two independent attempts have success probabilities 1/5 and 4/5 Random variables and distribution functions
- A random variable X takes values 0, 1, and 3 with probabilities 1/2,1/3,1/6, respectively Expectation, moments, and transforms
- A sorting device independently sends each of six incoming pieces to tray A, B, or C… Joint distributions and conditional expectation
- Conditioning changes the interval on a triangular support Joint distributions and conditional expectation
- A weighted triangle is not uniform on its conditional slices Joint distributions and conditional expectation