A trader in the foreign exchange market forecasts the following EUR$/$USD exchange rates for the quarter as follows:

US$$1\mathrm{.}11$ with a probability of $0\mathrm{.}25$

US$$1\mathrm{.}13$ with probability $0\mathrm{.}50$

US$$1\mathrm{.}15$ with probability $0\mathrm{.}25$

The $90-$day forward rate is $$1\mathrm{.}12.$

$($a$)$ Will the forex trader buy or sell euro futures against dollars if he is only interested in expected prices? In what quantity?

$($b$)$ What is actually likely to limit the trader's speculative actions?

$($c$)$Suppose the trader revises his forecast as follows:

$$1\mathrm{.}09$ with probability $0\mathrm{.}33$

$$1\mathrm{.}13$ with probability $0\mathrm{.}33$

$$1\mathrm{.}17$ with probability $0\mathrm{.}33$

If the forward rate stays at $$1\mathrm{.}12,$ will his decisions be affected? Justify your answer