$(5$ pts$)$ Measurements from a memory system show that in $500$ memory references there are $450$ hits for the cache. Assume that the cache hit time is $2ns$ and it is the same as the processor's clock cycle time. $($a$)$ What is the clock rate? $($b$)$ What is the average memory access time $($in terms of ns$)$ of the memory system with a miss penalty of $25$ cycles. $($c$)$ Suppose doubling the size of the cache reduces the miss rate to $6\%,$ but causes the miss penalty to increase to $50$ cycles. Is it beneficial to double the size of the cache? Why? Show your work!