The discrete random variable X X\,X has the probability distribution given in the first table below, where a a\,a and b b\,b are constants.
| xxx | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| P(X=x)P(X = x)P(X=x) | 0.12 | aaa | 0.31 | bbb |
Some cumulative probabilities for X X\,X are given in the second table below, where d d\,d and e e\,e are constants.
| xxx | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| P(X≤x)P(X\le x)P(X≤x) | 0.12 | 0.45 | ddd | eee |
Find the value of aaa.
Find the value of ddd.
Write down the value of eee.
Find the value of bbb.
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.