The discrete random variable X X\,X has probability function
P(X=x)=k(x+1)P(X=x)=k(x+1)P(X=x)=k(x+1) for x=0,1,2,3,4x=0,1,2,3,4x=0,1,2,3,4,
where k k\,k is a constant.
Find the exact value of kkk.
Find P(X is even)P(X\text{ is even})P(X is even).
Independent observations X1 X_1\,X1 and X2 X_2\,X2 have this distribution. Find P(X1=X2)P(X_1=X_2)P(X1=X2).
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.