Download presentation

Presentation is loading. Please wait.

Published bySarina Kingsbury Modified over 2 years ago

1
PROBABILITY DISTRIBUTION BUDIYONO 2011 (distribusi peluang)

2
RANDOM VARIABLES (VARIABEL RANDOM) Suppose that to each point of sample space we assign a real number We then have a function defined on the sample space This function is called a random variable or random function It is usually denoted by a capital letter such as X or Y

3
RANDOM VARIABLES (VARIABEL RANDOM) S = {AAA, AAG, AGA, AGG, GAA, GAG, GGA, GGG} The set of value of the above random variable is {0, 1, 2, 3} A random variable which takes on a finite or countably infinite number of values is called a discrete random variable A random variable which takes on noncountably infinite number of values ia called continous random variable

4
PROBABILITY FUNCTION (fungsi peluang) It is called probability function or probability distribution Let X is a discrete random variable and suppose that it values are x 1, x 2, x 3,..., arranged in increasing order of magnitude It assumed that the values have probabilities given by P(X = x k ) = f(x k ), k = 1, 2, 3,... abbreviated by P(X=x) = f(x)

5
PROBABILITY FUNCTION (fungsi peluang) X R 0.125 0.375 0.375 0.125 f random variable probability function A function f(x) = P(X = x) is called probability function of a random variable X if: 1.f(x) ≥ 0 for every x in its domain 2.∑ f(x) = 1

6
Can it be a probability function? On a sample space A = {a, b, c, d}, it is defined the function: a. f(a) = 0.5; f(b) = 0.3; f(c) = 0.3; f(d) = 0.1 b. g(a) = 0.5; g(b) = 0.25; g(c) = 0.25; g(d) = 0.5 c. h(a) = 0.5; h(b) = 0.25; h(c) = 0.125; h(d) = 0.125 d. k(a) = 0.5; k(b) = 0.25; k(c) = 0.25; k(d) = 0 Solution: a. f(x) is not a probability function, since f(a)+f(b)+f(c)+f(d) 1. b. g(x) is not a probability function, since g(c) 0. c. h(x) is a probability function. d. k(x) is a probability function.

7
DENSITY FUNCTION (fungsi densitas) It is called probability density or density function A real values f(x) is called density function if: 1. f(x) ≥ 0 for every x in its domain 2. It is defined that: P(a

8
Can it be a density function? a. No, it is not. Since f(x) may be negative b. No, it is not. Since the area is not 1 c. Yes, it is. If the area is 1 area = 1 d. Yes, it is. If the area is 1 area = 1

9
Solution: (2,0) area = 1

10
Solution: (2,0)

11
Solution:

13
Distribution Function for Discrete Random Variable

14
Solution

15
Distribution Function for Continuous Random Variable Example

16
Solution:

17
MATHEMATICAL EXPECTATION (nilai harapan)

18
Solution:

19
MATHEMATICAL EXPECTATION (nilai harapan)

20
Solution:

21
The Mean and Variance of a Random Variable

22
Solution: So, we have:

23
Solution: So, we have:

Similar presentations

OK

Random Variables A random variable is a rule that assigns exactly one value to each point in a sample space for an experiment. A random variable can be.

Random Variables A random variable is a rule that assigns exactly one value to each point in a sample space for an experiment. A random variable can be.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on 8th 5 year plan india Mp ppt online registration 2012 Ppt on management by objectives peter Ppt on landing gears Ppt on step down transformer Ppt on power sharing in india download movies Ppt on edge detection algorithm Ppt on digital image processing gonzalez Ppt on site selection of thermal power plant Ppt on natural resources in india