Probability distributions, expectation and variance

Get into the exponential distribution through an exploration of its pdf.

Can you work out the means of these distributions using numerical methods?

How do you choose your planting levels to minimise the total loss at harvest time?

How do scores on dice and factors of polynomials relate to each other?

Can you build a distribution with the maximum theoretical spread?

Are these statistical statements sometimes, always or never true? Or it is impossible to say?

How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?

Typical survey sample sizes are about 1000 people. Why is this?

When is an experiment described by the binomial distribution? Why do we need both the condition about independence and the one about constant probability?

Are these scenarios described by the binomial distribution?