1 Pertemuan 10 Fungsi Kepekatan Khusus Matakuliah: I0134 – Metode Statistika Tahun: 2007

2 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 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 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)

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

6 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,

7 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

8 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

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

10 Short-cut Formula for Variance

11 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.

12 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,

13 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?

14 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

15 Percentiles Let p be a number between 0 and 1. The (100p)th percentile of the distribution of a continuous rv X denoted by, is defined by

16 Median The median of a continuous distribution, denoted by, is the 50 th percentile. So satisfies That is, half the area under the density curve is to the left of

17 Selamat Belajar Semoga Sukses.