Assignment #$4$

Random Number Generator & LCGs

Problem $1.$ Consider an $LCG,Z_{i+1}=(a{Z}_i+35)(mod1872).$ Find the smallest value of

multiplier a such that the LCG has full period.

Problem $2.$ Consider the PMMLCG

$(1)$ What is the possible maximal period length?

$(2)$ Find a value of a such that the PMMLCG has the maximal period.

Problem $3.$ Use the PMMLCG $Z_{i+1}=(16807Z_i)(mod(2^{31}-1))$ with

to do the following:

$(1)$ Generate $5000$ random numbers $U_i.$

$(2)$ Let

for $i=1,$dots,$5000.$

$(3)$ Use Input Analyzer to perform goodness$-$of$-$fit on $x_i.$

$(4)$ What is the best$-$fitted distribution?

Problem $4.$ Use Excel's RAND$()$ to redo Problem $3.$