Probability distributions, expectation and variance

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

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

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

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

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

Can you build a distribution with the maximum theoretical spread?

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

Use your skill and judgement to match the sets of random data.