Question

pls use the geogebra application to answer question 2 for me

QUESTION 2 Verify whether f(x) is a probability density function (pdf) by going through the following steps. a. Enter the entries in the table into the spreadsheet view in GeoGebra b. Plot all pairs of points (x,f(x)) and fit an appropriate curve or polynomial to the points. c. Show, by shading, the region corresponding to the area under f(x) for the range of x values 0 SXS 4. d. Using an appropriate GeoGebra command, find the area enclosed. e. Is the function a probability density function? Give reasons. Calculating Probabilities, if possible If the function was found to be a pdf, f. Shade the region enclose by f(x) and the subintervals i. 25x53 g. Use GeoGebra to find the probability that x lies within the interval i. 25x33 ii. x1 Analytic Verification Using an appropriate technique of integration, verify the answers obtained in (g) (detailed written solution required) X f(x) 0 0.5 0.5 0.4375 0.375 1.5 0.3125 2 0.25 2.5 0.1875 3 3.5 0.0625 4 0 0.125

Answer 1

(a) Click on View select spreadsheet and enter the data it may look rounded off but you can click on any box and see value in the formula bar at the top.

GeoGebra Classic 5 File Edit View Options Tools Window Help A {1,2} & © Algebra X Graphics X 6 Spreadsheet fx B B2 22 =0.4375 5 А B с 1 0 0.5 2 0.5 4 0.44 3 1 0.38 0.31 4 1.5 3 5 2 0.25 0.19 6 2.5 2 7 3 0.13 8 3.5 0.06 1 9 4 0 10 11 -4 -3 -2 - 1 0 1 2 3 4 5 6 7 8 9 10 11 12 12 13 14 15 -2 16 17 -3 18 19 20 -4 21 22 -5 Input: o Type here to search 1 PL E W х Ad 2) / ENG 7:14 PM 31-Jul-20

(b) select A and B column and click on the list of points from dropdown

GeoGebra Classic 5 File Edit View Options Tools Window Help A © Algebra Graphics {1,2} List 6 Spreadsheet fx| BI A1 22=0 {...} List of Points 5 A B с 1 0 0.5 12 34 Matrix 2 4 0.5 0.44 3 1 0.38 12 34 Table 4 1.5 0.31 3 5 2 0.25 Polyline 6 2.5 0.19 2 7 3 0.13 8 3.5 0.06 9 4 0 1 AB 0 С D E 10 F G H O 11 -4 -3 -2 -1 0 1 2 3 5 6 7 8 9 10 11 12 12 13 14 15 -2 16 17 -3 18 19 20 -4 21 22 -5 < Input: o Type here to search 1 PL E W х Ad 2) / ENG 7:15 PM 31-Jul-20

you will see all point and the list l1

GeoGebra Classic 5 File Edit View Options Tools Window Help A Σ © Spreadsheet fx B 6 A1 22=0 5 A B с Algebra X Graphics A = (0, 0.5) B = (0.5, 0.44) . C = (1, 0.38) D = (1.5, 0.31) E=(2, 0.25) F = (2.5, 0.19) G=(3, 0.13) • H= (3.5, 0.06) I = (4,0) 11 = {(0, 0.5), (0.5, 0.44), (1, 0.38 1 0 0.5 2 0.5 0.44 4 3 1 0.38 4 1.5 0.31 3 5 2 0.25 6 2.5 0.19 2 7 3 0.13 8 3.5 0.06 1 9 4 0 A B С D E 10 0 F G H O 11 -4 -3 -2 -1 0 1 2 3 5 6 7 8 9 10 11 12 12 13 14 15 -2 16 17 -3 18 19 20 -4 21 22 -5 < < Input: Type here to search o PL E W х AM 0 ) / ENG 7:16 PM 31-Jul-20

use this command to fit line FitLine( <List of Points> )

in place of list of points put l1

equation of line will be shown and you will see the line drawn as well.

(c) To shade the region

click view input bar from the view options and enter the following function to shade the area.

Shaded= UpperSum( <Function>, <Start x-Value>, <End x-Value>, <Number of Rectangles> )

Shaded= UpperSum( f,,0,4,1000)

rectangles are for approximation higher the number better approximation of the area

(e) you will see that the area is displayed as 1. Which is true if the function is PDF. Therefore, the given function is a Probability Density Function.

(d) You can also use the integral function for the area

Area=Integral(f, 0, 4)

GeoGebra Classic 5 File Edit View Options Tools Window Help A a=2 X Spreadsheet fx B 1 IEEE B 2 v 5 A B с 1 0 0.5 Algebra X Graphics • A = (0, 0.5) B = (0.5, 0.44) . C= (1, 0.38) • D = (1.5, 0.31) E=(2, 0.25) F = (2.5, 0.19) G=(3, 0.13) H= (3.5, 0.06) I = (4,0) 11 = {(0, 0.5), (0.5, 0.44), (1, 0.38 f: y = -0.13x + 0.5 Shaded = 1 Area = 1 2 0.5 0.44 4 3 1 0.38 4 1.5 0.31 3 5 2 0.25 6 2.5 0.19 2 7 3 0.13 8 3.5 0.06 Area = 1 1 9 4 0 f A в с D E 10 F G H 11 -4 -3 -2 - 1 0 1 2 3 7 8 9 10 11 12 12 Shaded = 1 13 14 15 -2 16 17 -3 18 19 20 -4 21 22 -5 < Input: Type here to search o PL E W х AM 0 ) / ENG 7:23 PM 31-Jul-20

2 A B C D E F G H I نیا -2 -1 0 3 2 Shaded = 1 -1

As per HOMEWORKLIB POLICY we can answer only the first 4 parts.

If it helps, kindly upvote.

Comment below for doubt.