The random variable X X\,X has the following probability distribution.
| xxx | 1 | 2 | 3 | 4 | 5 |
| P(X=x)P(X=x)P(X=x) | kkk | k2\displaystyle \frac{k}{2}2k | k3\displaystyle \frac{k}{3}3k | k4\displaystyle \frac{k}{4}4k | k5\displaystyle \frac{k}{5}5k |
where k k\,k is a constant.
Find the value of kkk.
The random variables X1 X_1\,X1 and X2 X_2\,X2 are independent and each have the same distribution as XXX. Find P(X1+X2=7)P(X_1 + X_2 = 7)P(X1+X2=7)
390 exam-style questions on OCR A Level Maths 2.4 Statistical Distributions, covering 2.4.1 Discrete probability distributions, 2.4.2 Binomial distribution as a model, 2.4.3 Calculating binomial probabilities, 2.4.4 Mean and variance of the binomial (A-level only), 2.4.5 Normal distribution as a model (A-level only), 2.4.6 Probabilities using the normal distribution (A-level only), 2.4.7 Links to histograms, mean and standard deviation (A-level only), and 2.4.8 Selecting an appropriate distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.