Why model of a system is built? What is static model? Differentiate between static and dynamic mathematical models in simulation.[10]

What is storage in GPSS? Describe the blocks associated to storage in GPSS. A machine tool in a manufacturing shop is turning out parts at the rate off one every 5 minutes. As they are finished the parts go on an inspector who takes $10 \pm 3$ minutes to examine each one and rejects $10\%$ of the parts. Represent the system in GPSS using the concept of facility and run the simulation for 500 parts.[10]

What are the two main properties of random numbers? Test whether the 3rd, 7th, 11th, and so on numbers in the sequence in the following random number sample are auto-correlated. $(Z_{\alpha}=0.05$ and $Z_{0.025}=1.96)$ 0.12, 0.01, 0.23, 0.28, 0.89, 0.31, 0.64, 0.28, 0.83, 0.93, 0.99, 0.15, 0.33, 0.35, 0.91, 0.41, 0.60, 0.27, 0.75, 0.88, 0.68, 0.49, 0.05, 0.43, 0.95, 0.58, 0.19, 0.36, 0.69, 0.87,[10]