I need help for answers to this questions:

3.1 The proportion of time per day that all checkout counters in a Foodlovers Market are busy is a random variable with a density function given by

()=6(1), 0<<1

0, elsewhere

Find the mean and standard deviation and interpret your answer.

3.2 Find the moment-generating function for an exponential-distributed random variable.?

3.3 Use the moment-generating function found in (3.2) to find E(Y) and ().?

3.4 Suppose that possesses the density function.

()= 2(2),02

0,elsewhere

with the mean = 2/3 and the variance = 2/9. Using Tchebysheff's theorem we find that:

(| - | 2)= (| - 2/3| 0.9428)= (-.2761 1.609).

3.4.3 Find the (-.2761 1.609)?

3.5 Consider a random variable Y with density function given by

()= 1/2 2/2, < < .

What type of distribution does follow?