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Responsi Teori Pendukung

Responsi Teori Pendukung . Pemodelan Stokastik. Hitung peluang. If three balls are drawn at random from a bag containing 6 red balls, 4 white balls, and 8 blue balls, what is the probability that : All three are red At least one is red One is red or two are white or two are blue .

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Responsi Teori Pendukung

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  1. Responsi Teori Pendukung Pemodelan Stokastik

  2. Hitung peluang • If three balls are drawn at random from a bag containing 6 red balls, 4 white balls, and 8 blue balls, what is the probability that : • All three are red • At least one is red • One is red or two are white or two are blue

  3. Peubah acak diskret • Suatu random-experiment berupa “tossing” duadadu. Jika X variabel random yang menyatakanjumlahdariduamatadadu yang muncul. Tentukan : • Fungsi massa peluang untuk X • E(X) dan Var(X)

  4. Peubah acak kontinu • Suatu peubah acak kontinu X mempunyai fungsi padat peluang : • Hitunglah : • Nilai c • P(0,5 ≤ x ≤ 0,75) • Fungsi Distribusi dari X, F(x) • Var(X)

  5. Some important random variables • Messages arrive at a computer at an average rate of 15 messages per second. The number of messages that arrive per second is known to be a Poisson random variable. Find the probability that : • No messages arrive in a second • More than 10 messages arrive in 1 second period

  6. Some important random variables • NilaiujianuntukmatakuliahStatistikadiikutisebuahUniversitasSwastamempunyai rata-rata nilaiujian = 58 danvariansi 100. Biladistribusinilaiujiandianggapberdistribusi normal, maka : • Bilanilaiujianuntuk lulus adalah 53,5, berapapersen yang tidak lulus • Bilaterdapat 15% mahasiswa yang memperolehnilai A, makaberapanilai minimal untukmemperolehnilai A

  7. Some important random variables • Andaikan peubah acak X~GEO(p) dan Y~EXP(θ). Tentukan θ sehingga • Peubahacak X berdistribusieksponensialdenganfpp : Hitungnilai k Hitung P(X ≤ 1)

  8. Bivariate • Dari 8 orangmahasiswa yang terdiridari 2 orangmahasiswafakultasSains, 3 orangmahasiswadariFakultasRekayasaIndustri, dan 3 orangmahasiswaFakultasElektrodanKomunikasi, akandipilih 4 orangsecaraacakuntukmendapatkanbeasiswa. Andaikanpeubahacak X menyatakanbanyaknyamahasiswaFakultasSains yang terpilih, danpeubahacak Y menyatakanbanyaknyamahasiswadariFakultasElektrodanKomunikasi yang terpilih, makatentukan : • Fungsi Massa Peluanggabungandari X dan Y • Var(X+Y)

  9. Bivariate • Diberikan fungsi massa peluang gabungan (joint pmf) dari bivariat X,Y : • Periksa apakah X dan Y independen • Hitung Cov(X,Y)

  10. Bivariate • Consider the bivariate density : • Obtain the appropriate constant c. • Obtain the marginal densities for X and Y, and calculate their means and variances • Obtain the covariance between X and Y, and check whether the random variables are independent

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