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

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

2 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 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 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 5 Exponential distribution X is said to have the exponential distribution if for some

6 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 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 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 9 Variance and Standard Deviation The variance of continuous rv X with pdf f(x) and mean is The standard deviation is

10 10 Short-cut Formula for Variance

11 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 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 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 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 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 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 17 Selamat Belajar Semoga Sukses.