The random variable Y Y\,Y represents the number of books borrowed by a student in one month. It has the following probability distribution.
| yyy | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| P(Y=y)P(Y=y)P(Y=y) | 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 Y1 Y_1\,Y1 and Y2 Y_2\,Y2 are independent and each have the same distribution as YYY. Find P(Y1+Y2=7)P(Y_1+Y_2=7)P(Y1+Y2=7).
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.