Question $2.$ Consider the linear congruential generator $($LCG$)x_i=(x_{i-1}+c)modm.$

$($a$)$ What are the necessary and sufficient conditions $($if any$)$ for this LCG to have full period?

$($b$)$ Generate the full sequence of random numbers using this LCG with $c=7,m=8,$ and seed $3.$

$($c$)$ Do you think this LCG can be used in practice? Why or why not?

$($d$)$ A friend of yours claims that any arbitrary LCG always generates random numbers that are correlated

even when it has the appropriate parameters, particularly a large modulus. Is this true? If so$,$ would it

cause any problems in a simulation experiment?