Babies with a particular congenital disorder are born in a large maternity hospital at a rate of two per four-week accounting period (FWAP). In any given FWAP what is the probability that more than three babies with this condition will be born in the hospital?

A group of individuals contains ten people with blood group O, five with group A and five with group B. Give a formula for the probability that a random sample of size six will contain two people with each blood group.

An athlete conceals two performance enhancing tablets in a bottle containing eight vitamin tablets that are similar in appearance. If three tablets are selected at random for testing by drugs surveillance officials, what is the probability the cheating will be detected? You may assume that analysis is not error prone, i.e. if a performance enhancing... Read More

Locate the global maximum point on the curve $y=xe^{-x^2}$.

Find the inflexion point on $y=e^{-x^2}$.

Prove that $1 + x < e^x < \frac{1}{1-x}$ for all $x\in(0,1)$.

Prove that $e^a (b-a) < e^b – e^a < e^b(b-a)$ for all $a<b$ in $\mathbb{R}$.

Consider the non-zero real-valued function $exp$ on the reals such that $exp(a+b)=exp(a)exp(b)$ and $exp'(a)=exp(a)$ for all real values of $a$ and $b$. Prove that this function is strictly increasing.

Where does the following converge $\int_{1}^{\infty} e^{-\alpha x} dx$?

For what values of $\alpha$ will $\int_1^\infty \! x^{-\alpha} \, \mathrm{d}x$ converge?