Bacteria are grown in a dish for a length of time (in hours) T which is a random variable with a uniform distribution over the range 5 to 6; that is, it has the pdf

F(t) = {1, 5<= t <=6} {0, otherwise}

the number of bacteria Y, in the dish is given by Y = e^(cT) where c is a positive constant.

(i) Write down the cdf of T and hence find the cdf of Y

(ii) Sketch both these cdfs

(iii) Differentiate the cdf of Y to find and sketch the pdf of Y

(iv) Also use the method of transformations to find the pdf of Y directly from the pdf of T.

(ii) and (iii) I should be able to do but i need help with (i) and (iv).

Thanks