Pertanyaan

Diketahui tabel distribusi probabilitas dari variabel acak X sebagai berikut Diketahui μ = 1,9. Sehingga dari tabel di atas, didapatkan nilai σ 2 = ...

Diketahui tabel distribusi probabilitas dari variabel acak X sebagai berikut

Diketahui μ = 1,9. Sehingga dari tabel di atas, didapatkan nilai $σ^{2} =$ ...

1,49
1,54
1,94
1,99
2,04

A. Khairunisa

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Pembahasan

Perhatikan bahwa

$begin mathsize 12px style sigma squared equals E open parentheses X minus mu close parentheses squared equals sum from i equals 1 to n of open parentheses x subscript i minus mu close parentheses squared f open parentheses x subscript i close parentheses equals sum from i equals 1 to n of open parentheses x subscript i minus 1 , 9 close parentheses squared f open parentheses x subscript i close parentheses equals open parentheses 0 minus 1 , 9 close parentheses squared open parentheses 0 , 2 close parentheses plus open parentheses 1 minus 1 , 9 close parentheses squared open parentheses 0 , 1 close parentheses plus open parentheses 2 minus 1 , 9 close parentheses squared open parentheses 0 , 4 close parentheses plus open parentheses 3 minus 1 , 9 close parentheses squared open parentheses 0 , 2 close parentheses plus open parentheses 4 minus 1 , 9 close parentheses squared open parentheses 0 , 1 close parentheses equals open parentheses negative 19 over 10 close parentheses squared times 2 over 10 plus open parentheses negative 9 over 10 close parentheses squared times 1 over 10 plus open parentheses 1 over 10 close parentheses squared times 4 over 10 plus open parentheses 11 over 10 close parentheses squared times 2 over 10 plus open parentheses 21 over 10 close parentheses squared times 1 over 10 equals 361 over 100 times 2 over 10 plus 81 over 100 times 1 over 10 plus 1 over 100 times 4 over 10 plus 121 over 100 times 2 over 10 plus 441 over 100 times 1 over 10 equals fraction numerator 722 over denominator 1.000 end fraction plus fraction numerator 81 over denominator 1.000 end fraction plus fraction numerator 4 over denominator 1.000 end fraction plus fraction numerator 242 over denominator 1.000 end fraction plus fraction numerator 441 over denominator 1.000 end fraction equals fraction numerator 1.490 over denominator 1.000 end fraction equals 1 comma 49 end style$