Exercise Variabel Random Hal 83 [PDF]

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Rifky Ardhana K. 0401516031



EXERCISE VARIABEL RANDOM BUKU INTRODUCTION TO PROBABILITY AND MATHEMATICAL STATISTICS LEE J. BAIN 1. Let e = ( I, j ) represent an arbitrary outcome resulting from two rolls of the foursided die of Example 2.1.1. Tabulate the discrete pdf and sketch the graph of the CDF for the following random variables : (a) Y (e) = i + j. (b) Z (e) = i – j. (c) W (e) = (i – j)2 Jawaban: Ruang sampel: S = {(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (3, 4), (4, 1), (4, 2), (4, 3), (4, 4)} n(S) = 16 (a) Y (e) = i + j. Y (e) Titik sampel fyy (var. (Fkp) Rand.) 1 2 (1, 1) 16 3



(1, 2), (2, 1)



2 16



4



(1, 3), (2, 2), (3, 1)



3 16



5



(1, 4), (2, 3), (3, 2), (4, 1)



4 16



6



(2, 4), (3, 3), (4, 2)



3 16



7



(3, 4), (4, 3)



2 16



8



(4, 4)



1 16



Rifky Ardhana K. 0401516031 1 16 2







16 3



Fungsi pdf : fy y =



16



, y = 2, y = 8 , y = 3, y = 7 , y = 4, y = 6 4 16



{



1



16 6



Fungsi CDF: Fy y =



16 10 16 13 16 15 16



{ 



y=5



0 y lainnya 0, y < 2 16 3







,



, 2≤y