TD - Normally distributed risky assets and their mean and variances

QUESTION
Consider a portfolio of 4 risky assets X(1)
, X(2) which are held in proportion
θ1 and θ2 = 1 − θ1. Let them be distributed normally with µ1, µ2 and
variance σ
2
1
, σ
2
2
respectively.
(a) Show that the mean value of the portfolio is µ = θ1µ1 + θ2µ2.
(b) Show that if the prices of the risky assets are uncorrelated, then the
variance of the portfolio is given by θ
2
1σ
2
1 + θ
2
2σ
2
2
.
(c) Show that if the prices of the risky assets have some correlation then
the variance is given by θ
2
1σ
2
1 + θ
2
2σ
2
2 + 2θ1θ2ρ12 where the correlation
between the prices ρ12 = hX(1)X(2)i − µ1µ2.
(d) Given the following data evaluate the mean and variance of the portfolio:
µ1 − 0.2, σ1 = 0.75, µ2 = 0.16, σ2 = 0.5, ρ12 = −0.60.