If x and y are independent continuous positive random
variables, express the density function of (a) z=x/y and (b) z=xy in
terms ofthe density functions of x and y. evaluate these
expressions in thespecial case where x and y are both exponential
randomvariables.

a) has CDF

where the last equality follows from independence of . In terms of the distribution and density functions of , this is

Then the density is obtained by differentiating with respect to ,

b) can be computed in the same way; it has CDF

Differentiating gives the associated PDF,

Assuming and , we have

and

I wouldn't worry about evaluating this integral any further unless you know about the Bessel functions.

594 square inches

step-by-step explanation:

vote !

a, b, c, d are correct.

step-by-step explanation:

we have g(x) = 3 and are required to find which option is a translation of g(x).

now, 'translation' is a transformation which means to shift the function in any direction and the general form of translation is g(x) + k, where k is any real number.

so, according to the options we see that all are correct as they satisfy the general form of translation.

also, it can be seen from the graph below that the function g(x) = 3 is shifted from its position in all the four options.