Question $4$

Payoff, $x$

i$)$ Calculate the expected payoffs and variances of the playoffs for the two assets.

$(4)$

ii$)$ Calculate the covariance and correlation between the payoffs on the two assets.

$(4)$

iii$)$ Suppose that the investor does not know the value of $x.$ What is the expected payoff

on the asset?

iv$)$ Suppose that the investor knows that $x=4.$ What is the expected payoff on the asset

$($i$.$e$.$ calculate $E[Y|x=4])?$ What is the expected payoff if $x=6($i$.$e$.$

calculate $E[Y|x=6]?$

v$)$ Calculate $E[E[Y|x]]$