Examples and practice
Discrete random variables
Back to lessonPractice section 1 · Questions 1–6
Sum two tetrahedral dice · Complete a distribution and read inequalities · +4 more
Practice section 2 · Questions 7–12
Use the midpoint convention for a median · Find a mean by symmetry and by summation · +4 more
Practice section 3 · Questions 13–18
Transform a mean and variance · Distinguish a transformed observation from two independent observations · +4 more
Practice section 4 · Questions 19–24
Separate the two-card stopping cases from the squared third-card scores · Count products with their multiplicities before calculating moments · +4 more
- Separate the two-card stopping cases from the squared third-card scores
- Count products with their multiplicities before calculating moments
- Put the squared deviation inside the expectation
- Normalise the parameterised distribution before transforming variance
- Distinguish a reflected distribution from dependent realised throws
- Count heads across the stopping rule before setting a fair fee
Practice section 5 · Questions 25–30
Separate disjoint prizes and subtract the entry fee once · Score three draws without replacement · +4 more
- Separate disjoint prizes and subtract the entry fee once
- Score three draws without replacement
- Normalise the maximum score and count three-round orderings
- Use a weighted difference grid for two independent totals
- Average absolute values and build the sum distribution
- Use the absolute deviation and avoid double-counting the double-two case
Practice section 6 · Questions 31–36
Follow the reroll rule and translate a difference into an absolute value · Take fourth moments when an area is proportional to the square · +4 more
- Follow the reroll rule and translate a difference into an absolute value
- Take fourth moments when an area is proportional to the square
- Respect the first-miss stopping rule before comparing rounds
- Retain the exceptional all-blue score in the conditional game
- Average the reciprocal score and distinguish gains from guesses
- Separate signed attack advantage from damage clipped at zero
Practice section 7 · Question 37
Count first-winning throws and distinguish payout from net gain