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 (MEI) A Level Maths 2.4 Probability Distributions, covering 2.4.1 Recognise binomial situations, 2.4.2 Probability of success p, 2.4.3 Calculate binomial probabilities, 2.4.4 Mean of the binomial distribution, 2.4.5 Expected frequencies for binomial, 2.4.6 Probability functions and discrete random variables, 2.4.7 Numerical probabilities for a simple distribution, 2.4.8 Normal distribution as a model (A-level only), 2.4.9 Shape of the Normal curve (A-level only), 2.4.10 Linear transformation and standardising (A-level only), 2.4.11 Symmetry and inflection of Normal curve (A-level only), 2.4.12 Calculate probabilities from a Normal distribution (A-level only), 2.4.13 Model with probability distributions, and 2.4 Probability Distributions. Each one has a worked solution and a mark scheme showing where the marks go.