Chapter 11.3, Problem 17PPS

To determine

To find: The investment advised to Carmen to choose.

Answer to Problem 17PPS

The investment advised to Carmen to choose is Fund A

Explanation of Solution

Given:

For Fund A,

30% chance of a $1900 profit

30% chance of a $600 profit

15% chance of a $200 loss

25% chance of a $500 loss

For Fund B,

40% chance of a $1600 profit

10% chance of a $900 profit

10% chance of a $300 loss

40% chance of a $400 loss

Calculation:

Calculate the value of $E\left(X\right)$ for fund A,

  $\begin{array}{c}E\left(X\right)=\$1900\left(0.3\right)+\$600\left(0.3\right)-\$200\left(0.15\right)-\$500\left(0.25\right)\\ =\$595\end{array}$

The value of the variance and the standard deviation for fund A is calculated in table.

$X$	$P\left(X\right)$	${\left(X-E\left(X\right)\right)}^2$	${\left(X-E\left(X\right)\right)}^{2}P\left(X\right)$
$1900	0.30	1703025	510907.5
$600	0.30	25	7.5
-$200	0.15	632025	94803.75
-$500	0.25	1199025	299756.25
Variance	=	$\sum \left[{\left(X-E\left(X\right)\right)}^{2}P\left(X\right)\right]$	905475
Standard deviation	=	$\sqrt{\sum \left[{\left(X-E\left(X\right)\right)}^{2}P\left(X\right)\right]}$	951.5645012

Calculate the value of $E\left(X\right)$ for fund B,

  $\begin{array}{c}E\left(X\right)=\$1600\left(0.3\right)+\$900\left(0.1\right)-\$300\left(0.1\right)-\$400\left(0.4\right)\\ =\$540\end{array}$

The value of the variance and the standard deviation for fund B is calculated in table.

$X$	$P\left(X\right)$	${\left(X-E\left(X\right)\right)}^2$	${\left(X-E\left(X\right)\right)}^{2}P\left(X\right)$
$1600	0.430	1123600	449440
$900	0.10	129600	12960
-$300	0.10	705600	70560
-$400	0.40	883600	353440
Variance	=	$\sum \left[{\left(X-E\left(X\right)\right)}^{2}P\left(X\right)\right]$	886400
Standard deviation	=	$\sqrt{\sum \left[{\left(X-E\left(X\right)\right)}^{2}P\left(X\right)\right]}$	941.4881837

Both have almost same standard deviation but Fund A has higher expected value so, Fund A will be chosen.

Thus,the investment advised to Carmen to choose is Fund A