Generating Random Numbers

wlmi

New Member
Hi guys i have a couple of Qs regarding generating random numbers:

1.
Suppose you are given only 3 very basic tools:
• a uniform random number table,
• the standard normal table, and
• a basic scientific calculator.

Explain how you would generate some lognormal random numbers. For simplicity, just take the parameters μ=0, and σ=1. You may either explain in words, or use an example to illustrate.

I said something like get the uniform random number (e.g. 7) and divide it by 10 (giving 0.7) and then find the corresponding Z value from the standard normal table (0.7 gives a Z of roughly 0.53). This is a normal random number so take the exp{} of it to give a lognormal random number. Any of this right???

2.
X and Y are independent random variables distributed uniformly in the interval (0,1). Let Z be a random variables defined by Z = X ×Y. Also let U = log(X), V = log(Y), and W = log(Z), where log( ) denotes the natural logarithm.
pdf of Z is -log{z} 0<z<1 .

a) Discuss about generating random number of Z. Do NOT write more than 5 lines.

For this i was thinking of finding the inverse of the CDF of Z and equating it to U~(0,1) and solving for Z, but i cant seem to solve this equation.

b)Suppose you are to generate many (say over 10 thousand) random numbers of Z, and then make a histogram of these random numbers. Without actually doing the simulation, sketch the approximate shape of the histogram you expect.

I have no idea for this one.

I'd appreciate any help.

Thanks guys.