$1.$ From July $2023$ until now the target FFR is $5\mathrm{.}25-5\mathrm{.}50($in computation use $5\mathrm{.}50).$ Due to recent news about inflation, on Sep $11,$ there is bp and a $15\%$ probability that it will lower it by $50$ bp$.$ Two weeks ago an $85\%$ probability, that on September $18$ the Federal Reserve would lower the Fed Funds Rate $($FFR$)$ by $25,$ the probability of the Fed lowering the target rate by $25$ bp was $66\%.$ What was the rate implied by the Fed Funds Futures two weeks ago and what is it today?