Compute estimates for the mean ˆµGOOG and volatility ˆσGOOG for Google (GOOG) and mean ˆµAAPLand volatility ˆσAAPL for Apple, Inc. (AAPL) using the historical price data in the spreadsheetsGOOG.csv and AAPL.csv posted on the course website. Each file contains 20 recent daily close pricesfrom which you are to compute 19 daily returns Rn for 1 ≤ n ≤ 19. GOOG.csvAccountDashboardCoursesGroupsCalendarHistorySearchHelpMATH 176/ECON 135 > Files homeworkDatePrice2/27/23 $90.102/24/23$89.352/23/23$91.072/22/23 $91.802/21/23 $92.052/17/23$94.592/16/23$95.782/15/23$97.102/14/23$94.952/13/23$95.002/10/23 $94.862/9/23$95.462/8/23 $100.002/7/23 $108.042/6/23 $103.472/3/23$105.222/2/23$108.802/1/23 $101.431/31/23 $99.871/30/23 $97.95 AAPL.csvAccountDashboardOUCoursesGroupsCalendar<HistorySearchⒸHelpMATH 176 / ECON 135 > Files > homeworkPrice2/27/23 $147.922/24/23$146.712/23/23 $149.402/22/23 $148.912/21/23 $148.482/17/23 $152.552/16/23 $153.71Date2/15/23 $155.332/14/23$153.202/13/23 $153.852/10/23 $151.012/9/23 $150.872/8/23$151.922/7/23$154.652/6/23$151.732/3/23$154.502/2/23$150.822/1/23$145.431/31/23$144.291/30/23 $143.00

Given the historical price data of Google and Apple as Date Price GOOG AAPL 2/27/2023 90.10…

Answered: Compute estimates for the mean ˆµGOOG…

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Compute estimates for the mean ˆµGOOG and volatility ˆσGOOG for Google (GOOG) and mean ˆµAAPL
and volatility ˆσAAPL for Apple, Inc. (AAPL) using the historical price data in the spreadsheets
GOOG.csv and AAPL.csv posted on the course website. Each file contains 20 recent daily close prices
from which you are to compute 19 daily returns Rn for 1 ≤ n ≤ 19.

GOOG.csv
Account
Dashboard
Courses
Groups
Calendar
History
Search
Help
MATH 176/ECON 135 > Files homework
Date
Price
2/27/23 $90.10
2/24/23
$89.35
2/23/23
$91.07
2/22/23 $91.80
2/21/23 $92.05
2/17/23
$94.59
2/16/23
$95.78
2/15/23
$97.10
2/14/23
$94.95
2/13/23
$95.00
2/10/23 $94.86
2/9/23
$95.46
2/8/23 $100.00
2/7/23 $108.04
2/6/23 $103.47
2/3/23
$105.22
2/2/23
$108.80
2/1/23 $101.43
1/31/23 $99.87
1/30/23 $97.95

AAPL.csv
Account
Dashboard
OU
Courses
Groups
Calendar
<
History
Search
Ⓒ
Help
MATH 176 / ECON 135 > Files > homework
Price
2/27/23 $147.92
2/24/23
$146.71
2/23/23 $149.40
2/22/23 $148.91
2/21/23 $148.48
2/17/23 $152.55
2/16/23 $153.71
Date
2/15/23 $155.33
2/14/23
$153.20
2/13/23 $153.85
2/10/23 $151.01
2/9/23 $150.87
2/8/23
$151.92
2/7/23
$154.65
2/6/23
$151.73
2/3/23
$154.50
2/2/23
$150.82
2/1/23
$145.43
1/31/23
$144.29
1/30/23 $143.00

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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