Mathematics 7356: Statistical Distributions Topical Past Paper Questions

The discrete random variables X and Y can be modelled by the distributions X~ B(40, p) Y~ B(25, 0.6) It is given that the mean of X is equal to the variance of Y (a) Find the value of p [3 marks] (b) Find P(Y = 17)

The discrete random variable X has probability distribution The discrete random variable Y has probability distribution It is claimed that $\mathrm{P}(X \geq 3)$ is greater than $\mathrm{P}(Y \leq 4)$ Determine if this claim is correct. Fully justify your answer. [4 marks]

The discrete random variable X is modelled by the probability distribution defined by: $$ \mathsf{P}(X=x)=\left\{\begin{array}{c c}{c x}&{x=1,2}\\ {k x^{2}}&{x=3,4}\\ {}&{}\\ {0}&{\mathrm{o t h e r w i s e}}\\ \end{array}\right. $$ where k and c are constants. (a) State, in terms…