Factorise <img src="https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2B%2011x" id="TexFormula1" title="x^{2} + 11x" alt="x^{2} + 11x" alig

g100num [7]

A relation is (also) a function if every input x is mapped to a unique output y.

In terms of graphical representation, this implies that a graph represents a function if there doesn't exist a vertical line that intersects the graph more than once. So:

The first graph is exactly a vertical line, so it's not a function.
The second graph represents the function y=x, so it's a function: you can see that every possible vertical line crosses the graph only once.
The third graph is not a function, because you can draw vertical lines that cross the graph twice.
Similarly, in the fourth graph you can draw vertical lines that cross the graph twice
The fifth graph is a function, because every vertical line crosses the graph once
The last graph is a function, although discontinuous, for the same reason.

8 0

3 years ago

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What is the variance of a portfolio invested 21 percent each in a and b and 58 percent in c?

victus00 [196]

Given the following information:

$\begin{tabular}
{|p{1.5cm}|p{1.5cm}|p{1.2cm}|p{1.2cm}|p{1.2cm}|}
\multicolumn{1}{|p{1.5cm}|}{State of economy}\multicolumn{1}{|p{2.6cm}|}{Probability of State of economy}\multicolumn{3}{|p{4.8cm}|}{Rate of Return if State Occurs}\\[1ex] 
\multicolumn{1}{|p{1.5cm}|}{}\multicolumn{1}{|p{2.6cm}|}{}\multicolumn{1}{|c|}{Stock A}&StockB&Stock C\\[2ex]
\multicolumn{1}{|p{1.5cm}|}{Boom}\multicolumn{1}{|p{2.6cm}|}{0.66}\multicolumn{1}{|p{1.27cm}|}{0.09}&0.03&0.34\\
\end{tabular}$
$\begin{tabular}
{|p{1.5cm}|p{1.5cm}|p{1.2cm}|p{1.2cm}|p{1.2cm}|}
\multicolumn{1}{|p{1.5cm}|}{Bust}\multicolumn{1}{|p{2.6cm}|}{0.34}\multicolumn{1}{|p{1.27cm}|}{0.23}&0.29&-0.14\\
\end{tabular}$

Part A:

The expected return on an equally weighted portfolio of these three stocks is given by:

$0.66[0.33 (0.09) + 0.33 (0.03) + 0.33(0.34)] \\ +0.34[0.33 (0.23) + 0.33(0.29) +0.33(-0.14)] \\ \\ =0.66(0.0297 + 0.0099 + 0.1122)+0.34(0.0759+0.0957-0.0462) \\ \\ =0.66(0.1518)+0.34(0.1254)=0.1002+0.0426=0.1428=\bold{14.28\%}$

Part B:

Value of a portfolio invested 21 percent each in A and B and 58 percent in C is given by

For boom: 0.21(0.09) + 0.21(0.03) + 0.58(0.34) = 0.0189 + 0.0063 + 0.1972 = 0.2224 or 22.24%.

For bust: = 0.21(0.23) + 0.21(0.29) + 0.58(-0.14) = 0.0483 + 0.0609 - 0.0812 = 0.028 or 2.8%

Expected return = 0.66(0.2224) + 0.34(0.028) = 0.1468 + 0.00952 = 0.1563 or 15.63%

The variance is given by

$0.66(0.2224-0.1563)^2+0.34(0.028-0.1563)^2 \\ \\ =0.66(0.0661)^2+0.34(-0.1283)^2=0.66(0.00437)+0.34(0.01646) \\ \\ =0.00288+0.0056=\bold{0.00848}$