$($b$)$ Arina plans to form an investment portfolio that comprised of $50$ percent investment in share X$,25$ percent investment in share Y and $25$ percent in share Z$.$ The following are the estimated returns for all the three types of financial assets:

Year

Probability $($P$)$

Expected Return $(\%)$ of Financial Assets

X

Y

Z

Strong

$0\mathrm{.}48$

$10$

$15$

$20$

Weak

$0\mathrm{.}52$

$8$

$6$

$1$

Calculate:

i$.$ Expected return for each share.

ii$.$ Expected return for investment portfolio $($r$-$portfolio$)$ of share X$,$ Y and Z$.$

iii. Variance for the investment portfolio

iv$.$ Standard deviation for the investment portfolio.