PROBABILITY DISTRIBUTION BUDIYONO 2011 (distribusi peluang)
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Transcript of PROBABILITY DISTRIBUTION BUDIYONO 2011 (distribusi peluang)
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
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
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 x1, x2, x3, ..., arranged in increasing order of magnitude
It assumed that the values have probabilities given by P(X = xk) = f(xk), k = 1, 2, 3, ... abbreviated by P(X=x) = f(x)
PROBABILITY FUNCTION(fungsi peluang)
X
R• 0.125
• 0.375
• 0.375
• 0.125f
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
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) = 0.1b. g(a) = 0.5; g(b) = 0.25; g(c) = 0.25; g(d) = 0.5c. h(a) = 0.5; h(b) = 0.25; h(c) = 0.125; h(d) = 0.125d. 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.
DENSITY FUNCTION(fungsi densitas)
1dx)x(f
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<X<b) = P(a<X≤b) = P(a≤X<b) = P(a≤X≤b) =
b
adx)x(f
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 1area = 1
d.Yes, it is. If the area is 1
area = 1