Fungsi Kepekatan Peluang Khusus Pertemuan 10 Matakuliah : L0104 / Statistika Psikologi Tahun : 2008 Fungsi Kepekatan Peluang Khusus Pertemuan 10

Learning Outcomes Pada akhir pertemuan ini, diharapkan mahasiswa akan mampu : Mahasiswa akan dapat menghitung peluang, nilai harapan dan varians fungsi kepekatan seragam dan eksponensial. 3 Bina Nusantara

Outline Materi Fungsi kepekatan seragam Fungsi distribusi seragam Nilai harapan dan varians fungsi kepekatan seragam Fungsi kepekatan eksponensial Fungsi distribusi eksponensial Nilai harapan dan varians peubah acak eksponensial 4 Bina Nusantara

Uniform Distribution A continuous rv X is said to have a uniform distribution on the interval [a, b] if the pdf of X is X ~ U (a,b) Bina Nusantara

Exponential distribution X is said to have the exponential distribution if for some Bina Nusantara

Probability for a Continuous rv If X is a continuous rv, then for any number c, P(x = c) = 0. For any two numbers a and b with a < b, Bina Nusantara

Expected Value The expected or mean value of a continuous rv X with pdf f (x) is The expected or mean value of a discrete rv X with pmf f (x) is Bina Nusantara

Expected Value of h(X) If X is a continuous rv with pdf f(x) and h(x) is any function of X, then If X is a discrete rv with pmf f(x) and h(x) is any function of X, then Bina Nusantara

Variance and Standard Deviation The variance of continuous rv X with pdf f(x) and mean is The standard deviation is Bina Nusantara

Short-cut Formula for Variance Bina Nusantara

The Cumulative Distribution Function The cumulative distribution function, F(x) for a continuous rv X is defined for every number x by For each x, F(x) is the area under the density curve to the left of x. Bina Nusantara

Using F(x) to Compute Probabilities Let X be a continuous rv with pdf f(x) and cdf F(x). Then for any number a, and for any numbers a and b with a < b, Bina Nusantara

Ex 6 (Continue). X = length of time in remission, and What is the probability that a malaria patient’s remission lasts long than one year? Bina Nusantara

Obtaining f(x) from F(x) If X is a continuous rv with pdf f(x) and cdf F(x), then at every number x for which the derivative Bina Nusantara

Selamat Belajar Semoga Sukses. Bina Nusantara