Show that when f and g are both bijections.
1. Give a formal statement of the following models identifying the probability laws of the data and the parameter space. State whether the model in question is parametric or nonparametric.
(a) A geologist measures the diameters of a large number n of pebbles in an old stream bed. Theoretical considerations lead him to believe that the logarithm of pebble diameter is normally distributed with mean p, and variance He wishes to use his observations to obtain some information about
 but has in advance no knowledge of the magnitudes of the two parameters.
(b) A measuring instrument is being used to obtain n independent determinations of a physical constant
  Suppose that the measuring instrument is known to be biased to the positive side by 0.1 units. Assume that the errors are otherwise identically distributed normal random variables with known variance.
(c) In part (b) suppose that the amount of bias is pOsitive but unknown. Can you perceive any difficulties in making statements about  for this model?
(d) The number of eggs laid by an insect follows a Poisson distribution with unknown mean Once laid, each egg has an unknown chance p of hatching and the hatching of one egg is independent of the hatching of the others. An entomologist studies a set of n such insects observing both the number of eggs laid and the number of eggs hatching for each nest.