Suppose that we add an L$3$ cache to the system in problem $2$ that has a hit rateof $90\%$ and an access time of $40$ ns$.$ What is the AMAT for this scenario? Each access timeis for that particular component.$(10$ points$)$ Our storage consists only of L$1$ cache, L$2$ cache and RAM. L$1$ cache has an access time of $1ns$ and a hit rate of $80\%.$ L$2$ cache has an access time of $20ns$ and a hit rate of $85\%.$ RAM has an access time of $90ns.$ What is the AMAT for this scenario? Each access time is for that particular component.

$(10$ points$)$ Suppose that we add an L$3$ cache to the system in problem $2$ that has a hit rate of $90\%$ and an access time of $40ns.$ What is the AMAT for this scenario? Each access time is for that particular component. Please show the steps in detail.