Question

A perfect cubical dice is thrown 50 times. Record the number of times each face turns up. Let X denote the face of dice.

Show that E(2x -3) = 2E(X) - 3

Answer 1

Using Excel

randbetween(1,6) gives random integer between 1 and 6

X
1
3
4
6
3
1
2
6
3
1
5
4
5
6
1
5
5
6
4
5
4
5
5
1
3
2
5
5
2
4
6
3
4
2
4
6
6
4
2
2
6
4
6
2
6
6
4
3
4
2

X	Frequency
1	5
2	8
3	6
4	11
5	9
6	11

E(X) = 1*5/50 + 2 * 8/50 + 3 * 6/50 + 4*11/50 + 5 *9/50 + 6 *11/50

= 3.88

RHS = 2 * E(X) - 3 = 2 * 3.88 -3 = 4.76

p	2X-3
0.1	-1
0.16	1
0.12	3
0.22	5
0.18	7
0.22	9

E(2X -3) = (-1) *5/50 + 1 * 8/50 + 3 * 6/50 + 5*11/50 + 7 *9/50 + 9 *11/50

=4.76

LHS =RHS

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