4. Assume there exists some continuous variable X that is a function of time t. You are

told that the probability distribution function for X in the range 0 < t < oo is given

by:

f(t)

-

1

=-e

-t/to

to

where to is a characteristic time.

If to = 0. 667:

a. Sketch this probability distribution.

b. Show this probability distribution is normalised to 1.

C. Evaluate the mean of this distribution.

[4 marks]

[4 marks]

[4 marks]

[Q4 total: 12 marks]