Definisi: Variabel acak adalah variabel yang mengambil nilai berbeda dalam suatu percobaan acak.
Variabel acak kategoris (Nominal)
Contoh: Jenis Kelamin (laki-laki, perempuan), pekerjaan (PNS, pegawai perusahaan, pelajar, pensiunan, pengangguran), hasil tes (negatif, positif)
Variabel acak kategorikal yang diurutkan (Diurutkan)
Contoh: sikap (sangat setuju, setuju, netral, tidak setuju, sangat tidak setuju), frekuensi penggunaan (seminggu sekali, dua minggu sekali, enam bulan sekali, hampir tidak pernah, tidak pernah)
Variabel acak numerik
Contoh: Umur (13, 14, 15, 16...), penghasilan (bisa diisi nilai berapa saja)
2. Distribusi probabilitas diskrit
2.1 Distribusi Binomial
definisi: dijelaskan dalam tidak adaN Berhasil dalam uji coba independen kkaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaakuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu Peluang keberhasilan pada setiap percobaan adalah hal.P。
rumus： X ∼ Bin ( n , p ) X sim teks{Bin}(n, p)X∼Tempat sampah(N,P)
Fungsi Massa Probabilitas (PMF)： Bahasa Indonesia: P(X = k) = (nk) pk (1 − p) n − k P(X = k) = binomial{n}{k} p^k (1-p)^{nk}P(X=aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaakuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu)=(aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaakuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuN)Paaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaakuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu(1−P)N−aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaakuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu
Fungsi distribusi kumulatif (CDF)： F(X = k) = ∑ i = 0 k(ni) pi(1 − p) n − i F(X = k) = jumlah_{i=0}^{k} binom{n}{i} p^i (1-p)^{ni}F(X=aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaakuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu)=∑Saya=0aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaakuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu(SayaN)PSaya(1−P)N−Saya
2.2 Distribusi Bernoulli
definisi: Menjelaskan probabilitas keberhasilan (atau kegagalan) dalam suatu eksperimen hal.P。
rumus： X ∼ Bern ( p ) X sim teks{Bern}(p)X∼Kota Bern(P)
Fungsi Massa Probabilitas (PMF)： P ( X = x ) = { p jika x = 1 1 − p jika x = 0 P(X = x) ={PjikaX=11−PjikaX=0P(X=X)={P1−PjikaX=1jikaX=0
Fungsi distribusi kumulatif (CDF)： F ( X = x ) = { 0 jika x < 0 1 − p jika 0 ≤ x < 1 1 jika x ≥ 1 F(X = x) ={0jikaX<01−Pjika0≤X<11jikaX≥1F(X=X)=⎩⎨⎧01−P1jikaX<0jika0≤X<1jikaX≥1
2.3 Distribusi Geometris
definisi: Menjelaskan probabilitas jumlah kegagalan sebelum keberhasilan pertama hal.P。
rumus： X ∼ Geom ( p ) X sim teks{Geom}(p)X∼Geofisika(P)
Fungsi Massa Probabilitas (PMF)： Persamaan (1-p) kp adalah persamaan yang menyatakan hubungan antara P(X = k) dan (1-p)^kp.P(X=aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaakuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu)=(1−P)aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaakuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuP
Fungsi distribusi kumulatif (CDF)： Tentukanlah F(x) = 1 - (1 - p) k + 1!F(X=aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaakuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu)=1−(1−P)aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaakuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu+1
2.4 Distribusi Binomial Negatif
definisi: Menjelaskan jumlah kegagalan sebelum mencapai keberhasilan ke-r hal.P。
rumus： X ∼ NegBin ( r , p ) X sim teks{NegBin}(r, p)X∼NegBin(R,P)
Fungsi Massa Probabilitas (PMF)： Persamaan (1-p) k = p(x) = k + r - 1 kP(X=aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaakuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu)=(aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaakuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaakuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu+R−1)PR(1−P)aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaakuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu
Fungsi distribusi kumulatif (CDF)： F(X = k) = ∑ i = 0 k(i + r − 1 i) pr(1 − p) i F(X = k) = jumlah_{i=0}^{k} binom{i + r - 1}{i} p^r (1-p)^iF(X=aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaakuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu)=∑Saya=0aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaakuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu(SayaSaya+R−1)PR(1−P)Saya
2.5 Distribusi Hipergeometri
definisi: Menjelaskan pengambilan sampel dari populasi terbatas tanpa pengembalian tidak adaN kali, sukses kkaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaakuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu probabilitas kali.
rumus： X ∼ Hipergeom ( N , K , n ) X sim teks{Hipergeom}(N, K, n)X∼Hipergeom(N,Bahasa Inggris: Bahasa Inggris: Bahasa Inggris: Bahasa Inggris: Bahasa Inggris: K,N)
Fungsi Massa Probabilitas (PMF)： P ( X = k ) = ( K k ) ( N − K n − k ) ( N n ) P(X = k) = pecahan{binom{K}{k} binom{NK}{nk}}{binom{N}{n}}P(X=aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaakuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu)=(NN)(aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaakuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuBahasa Inggris: Bahasa Inggris: Bahasa Inggris: Bahasa Inggris: Bahasa Inggris: K)(N−aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaakuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuN−Bahasa Inggris: Bahasa Inggris: Bahasa Inggris: Bahasa Inggris: Bahasa Inggris: K)
Fungsi distribusi kumulatif (CDF)： F ( X = k ) = ∑ i = 0 k ( K i ) ( N − K n − i ) ( N n ) F(X = k) = jumlah_{i=0}^{k} pecahan{binom{K}{i} binom{NK}{ni}}{binom{N}{n}}F(X=aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaakuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu)=∑Saya=0aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaakuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu(NN)(SayaBahasa Inggris: Bahasa Inggris: Bahasa Inggris: Bahasa Inggris: Bahasa Inggris: K)(N−SayaN−Bahasa Inggris: Bahasa Inggris: Bahasa Inggris: Bahasa Inggris: Bahasa Inggris: K)
2.6 Distribusi Poisson
definisi: Deskripsi terjadi dalam satuan waktu kkaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaakuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu Peluang suatu kejadian, rata-rata laju terjadinya kejadian adalah λ.
rumus： X ∼ Poisson ( λ ) X sim teks{Poisson}(lambda)X∼Ikan(λ)
Fungsi Massa Probabilitas (PMF)： Misalkan x = k , maka x = k . P(X = k) = frak{lambda^ke^{-lambda}}{k!}P(X=aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaakuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu)=aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaakuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu!λaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaakuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuBahasa Inggris:−λ
Fungsi distribusi kumulatif (CDF)： F(X = k) = e − λ ∑ i = 0 k λ ii ! F(X = k) = e^{-lambda} jumlah_{i=0}^{k} pecahan{lambda^i}{i!}F(X=aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaakuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu)=Bahasa Inggris:−λ∑Saya=0aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaakuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuSaya!λSaya
2.7 Hubungan di antara mereka
Distribusi Bernoulliadalah spesialdistribusi binomial,Kapan n=1 n=1 adalah bilangan bulat positif yang paling kecil.N=1 jam.
distribusi geometrisadalah distribusi jumlah percobaan yang diperlukan sebelum keberhasilan pertama, yang dapat dipandang sebagaidistribusi binomialperpanjangan.
distribusi binomial negatifdapat dilihat sebagaidistribusi geometrisGeneralisasi , digunakan untuk menggambarkan jumlah kegagalan yang diperlukan sebelum r berhasil.
distribusi hipergeometriMirip dengandistribusi binomial, tetapi cocok untuk populasi terbatas dan pengambilan sampel tanpa pengembalian.
distribusi racunYadistribusi binomialKasus batas dari tidak adaN sangat besar dan hal.P sangat muda, dan λ = tidak ada lambda = tidak adaλ=NP tetap konstan.
3. Distribusi probabilitas berkelanjutan
3.1 Distribusi Eksponensial
definisi: Distribusi eksponensial adalah distribusi probabilitas kontinu yang sering digunakan untuk menggambarkan interval waktu antara kejadian independen.
rumus： X ∼ Eksponensial ( λ ) X sim text{Eksponensial}(lambda)X∼Eksponensial(λ),di dalam λ > 0 lambda>0λ>0 adalah parameter laju
Fungsi Kepadatan Probabilitas (PDF)： f ( x ; λ ) = λ e − λ x untuk x ≥ 0 f(x; lambda) = lambda e^{-lambda x} quad text{untuk } x geq 0F(X;λ)=λBahasa Inggris:−λXuntukX≥0
Fungsi distribusi kumulatif (CDF)： F ( x ; λ ) = 1 − e − λ x untuk x ≥ 0 F(x; lambda) = 1 - e^{-lambda x} quad text{untuk } x geq 0F(X;λ)=1−Bahasa Inggris:−λXuntukX≥0
3.2 Distribusi Gamma
definisi: Menjelaskan akumulasi waktu tunggu dan merupakan generalisasi dari distribusi eksponensial dan distribusi χ².
rumus： X ∼ Gamma ( k , θ ) X sim teks{Gamma}(k, theta)X∼Gamma(aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaakuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu,θ),di dalam k > 0 k > 0aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaakuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu>0 adalah parameter bentuk, θ > 0 theta>0θ>0 adalah parameter skala
Fungsi Kepadatan Probabilitas (PDF)： f ( x ; k , θ ) = xk − 1 e − x / θ θ k Γ ( k ) untuk x ≥ 0 f(x; k, theta) = frac{x^{k-1}e^{-x/theta}}{theta^k Gamma(k)} quad text{untuk } x geq 0F(X;aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaakuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu,θ)=θaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaakuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuΓ(aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaakuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu)Xaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaakuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu−1Bahasa Inggris:−X/θuntukX≥0,di dalam Gamma (k)Γ(aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaakuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu) adalah fungsi gamma
Fungsi distribusi kumulatif (CDF)： F(x; k, θ) = γ(k, x/θ) Γ(k) F(x; k, theta) = pecahan{gamma(k, x/theta)}{gamma(k)}F(X;aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaakuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu,θ)=Γ(aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaakuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu)γ(aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaakuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu,X/θ),di dalam γ ( k , x / θ ) gamma(k, x/theta)γ(aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaakuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu,X/θ) adalah fungsi gamma yang tidak lengkap.
3.3 Distribusi Normal
definisi: Menjelaskan distribusi jumlah sejumlah besar variabel acak independen dan banyak digunakan dalam ilmu alam dan ilmu sosial.
rumus： X ∼ N ( μ , σ 2 ) X sim matematika{N}(mu, sigma^2)X∼N(μ,σ2),di dalam, μ muμ adalah nilai rata-rata, σ 2 sigma^2σ2 adalah variansnya
Fungsi Kepadatan Probabilitas (PDF)： Bahasa Indonesia: f ( x ; μ , σ 2 ) = 1 2 π σ 2 e − ( x − μ ) 2 2 σ 2 f(x; mu, sigma^2) = pecahan{1}{akar{2pisigma^2}} e^{-frac{(x-mu)^2}{2sigma^2}}F(X;μ,σ2)=2πσ21Bahasa Inggris:−2σ2(X−μ)2
Fungsi distribusi kumulatif (CDF)： F ( x ; μ , σ 2 ) = 1 2 [ 1 + erf ( x − μ 2 σ 2 ) ] F(x; mu, sigma^2) = frac{1}{2}kiri[1 + namaoperator{erf}kiri(frac{x-mu}{sqrt{2sigma^2}}kanan)kanan]F(X;μ,σ2)=21[1+erf(2σ2X−μ)], dimana erf adalah fungsi kesalahan.
3,4 t-Distribusi
definisi: Digunakan untuk pengujian hipotesis dan estimasi interval kepercayaan dalam situasi sampel kecil.
rumus： X ∼ t ( ν ) X sim t(nu)X∼T(ν),di dalam, aku sekarangν adalah derajat kebebasan
Fungsi distribusi kumulatif (CDF)： Bahasa Indonesia: F ( t ; ν ) = 1 2 + t Γ ( ν + 1 2 ) π ν Γ ( ν 2 ) ∫ 0 t ( 1 + u 2 ν ) − ν + 1 2 du F(t; nu) = frac{1}{2} + tfrac{Gammaleft(frac{nu+1}{2}kanan)}{sqrt{pi nu} Gammaleft(frac{nu}{2}kanan)} int_0^{t} kiri(1 + frac{u^2}{nu}kanan)^{-frac{nu+1}{2}} duF(T;ν)=21+TπνΓ(2ν)Γ(2ν+1)∫0T(1+νkamkamu2)−2ν+1Dkamkamu
3.5 Distribusi Chi-Kuadrat
definisi: Biasa digunakan untuk pengujian hipotesis dan analisis varians.
rumus： X ∼ χ 2 ( k ) X sim chi^2(k)X∼χ2(aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaakuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu),di dalam kkaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaakuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu adalah derajat kebebasan
Fungsi Kepadatan Probabilitas (PDF)： f ( x ; k ) = 1 2 k / 2 Γ ( k / 2 ) xk / 2 − 1 e − x / 2 untuk x ≥ 0 f(x; k) = frac{1}{2^{k/2} Gamma(k/2)} x^{k/2-1} e^{-x/2} quad text{untuk } x geq 0F(X;aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaakuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu)=2aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaakuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu/2Γ(aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaakuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu/2)1Xaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaakuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu/2−1Bahasa Inggris:−X/2untukX≥0
Fungsi distribusi kumulatif (CDF)： F ( x ; k ) = γ ( k 2 , x 2 ) Γ ( k 2 ) F(x; k) = frac{gammaleft(frac{k}{2}, frac{x}{2}kanan)}{gammaleft(frac{k}{2}kanan)}F(X;aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaakuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu)=Γ(2aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaakuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu)γ(2aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaakuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu,2X)
3.6 Distribusi-F
definisi: Digunakan untuk membandingkan varian dua sampel.
rumus： X ∼ F ( d 1 , d 2 ) X simulasi F(d_1, d_2)X∼F(D1,D2),di dalam hari 1 hari_1D1 Dan hari ke 2 hari ke 2D2 adalah derajat kebebasan
Fungsi Kepadatan Probabilitas (PDF)： Bahasa Indonesia: f ( x ; d 1 , d 2 ) = ( d 1 x ) d 1 d 2 d 2 ( d 1 x + d 2 ) d 1 + d 2 x B ( d 1 2 , d 2 2 ) untuk x ≥ 0 f(x; d_1, d_2) = frac{akar akar{frac{(d_1 x)^{d_1} d_2^{d_2}}{(d_1 x + d_2)^{d_1 + d_2}}}}{x Bkiri(frac{d_1}{2}, frac{d_2}{2}kanan)} quad teks{untuk } x geq 0F(X;D1,D2)=XB(2D1,2D2)(D1X+D2)D1+D2(D1X)D1D2D2untukX≥0,di dalam BBB adalah fungsi beta
Fungsi distribusi kumulatif (CDF)： F ( x ; d 1 , d 2 ) = I d 1 xd 1 x + d 2 ( d 1 2 , d 2 2 ) F(x; d_1, d_2) = I_{frac{d_1 x}{d_1 x + d_2}}kiri(frac{d_1}{2}, frac{d_2}{2}kanan)F(X;D1,D2)=SAYAD1X+D2D1X(2D1,2D2),di dalam IISAYA adalah fungsi beta yang tidak lengkap
3.7 Hubungan di antara mereka
Distribusi chi-kuadratnya adalahjumlah kuadrat distribusi normal . Misalnya, kkaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaakuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu Jumlah kuadrat variabel normal standar bebas mengikuti derajat kebebasan sebagai kkaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaakuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu distribusi chi-kuadrat.
Distribusi t sudah masukDibangun berdasarkan distribusi normal standar dan distribusi chi-kuadrat dari. Secara khusus, distribusi t dapat diperoleh dengan membagi variabel normal standar dengan akar kuadrat dari variabel distribusi chi-kuadrat independennya.
Distribusi F adalahPerpanjangan rasio dua variabel independen yang terdistribusi chi-square . Distribusi F digunakan untuk membandingkan dua varian dan dibangun dengan mengambil rasio dua variabel yang terdistribusi chi-kuadrat.
