The random variable Z Z\,Z represents the number of goals scored by a team in a match. It has the following probability distribution.
| zzz | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| P(Z=z)P(Z=z)P(Z=z) | k2\displaystyle \frac{k}{2}2k | k3\displaystyle \frac{k}{3}3k | k4\displaystyle \frac{k}{4}4k | k5\displaystyle \frac{k}{5}5k | k6\displaystyle \frac{k}{6}6k |
where k k\,k is a constant.
Find the value of kkk.
The random variables Z1 Z_1\,Z1 and Z2 Z_2\,Z2 are independent and each have the same distribution as ZZZ. Find P(Z1+Z2=4)P(Z_1+Z_2=4)P(Z1+Z2=4).
57 exam-style questions on Edexcel AS Level Maths Statistical Distributions, covering 6.1 Probability Distributions, 6.2 The Binomial Distribution, and 6.3 Cumulative Probabilities. Each one has a worked solution and a mark scheme showing where the marks go.