$1.$ The following probability distribution shows the likelihood that an asset will yield the associated profits over $5$ days.

Profit Potential Probability

$16\%0\mathrm{.}60$

$8\%0\mathrm{.}20$

$13\%0\mathrm{.}12$

$14\%0\mathrm{.}04$

$11\%0\mathrm{.}04$

a$.$ What is the expected return?

b$.$ Compute the variance and standard deviation of the return

$2.$ What is the arithmetic average and variance of an investment with five year returns of $10\%,6\%,4\%,3\%$ and $-10\%.$

$3.$ Staples$$ stock has a $50\%$ chance of producing a $26\%$ return, a $30\%$ chance of producing a $11\%$ return, and a $20\%$ chance of producing a $32\%$ return. What is the firm's expected rate of return?

$4.$ Consider the following information:

State Probability Returns

Boom $0\mathrm{.}250\mathrm{.}15$

Normal $0\mathrm{.}500\mathrm{.}08$

Slowdown $0\mathrm{.}15-0\mathrm{.}05$

Recession $0\mathrm{.}10-0\mathrm{.}03$

a$.$ What is the expected return?

b$.$ What is the variance?

c$.$ What is the standard deviation?