A discrete random variable X X\,X has the probability distribution:
| xxx | 0 | 1 | 2 | 3 |
| P(X=x)P(X=x)P(X=x) | 0.2 | aaa | 0.3 | bbb |
Where a a\,a and b b\,b are constants.
The cumulative distribution F(x)F(x)F(x) of X X\,X is given below.
| xxx | 0 | 1 | 2 | 3 |
| F(x)F(x)F(x) | ccc | ddd | 0.78 | eee |
Where ccc, d d\,d and e e\,e are constants.
Find the values of aaa, bbb, ccc, d d\,d and eee.
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.