table of Contents
The concept of random variables
The concept : a random variable is a random phenomenon is the result of a variety of variables . The sides of the coin then 1,0 1,0 is the random variable.
Definition : YES sample space \ (\ Omega \) , and \ (\ Omega \ in \ Omega \) , \ (X-X-= (\ Omega ) \) is a real-valued function, then X is a random variable in the sample space, i.e., the sample space is mapped onto a set of real numbers.
Notation : event may represent a \ (\ = {X-A \} \) , the probability of the event can be expressed as: \ (P (= X-A), P \ {= X-A \} \)
Discrete random variables
Concept : discrete random variable \ (X-\) values may be a column, such as \ (x_k (k = 1,2,3 .... n) \)
- \ (The X-\) : represent variables
- \ (the X-\) : specific values.
Probability distribution (function)
\ (P \ {= X-x_k \} = P_K \) : probability function call / distribution satisfies the condition \ (P_k \ geq0, \ sum p_k = 1 \)
Continuous random variables
- Discrete -> probability distribution function
- Continuity -> probability density function
- Integral probability density function and probability distribution function (area) is 1.
Probability density function : nonnegative integrable function \ (f (x), f (x) \ geq 0, a \ leq b, if p \ {a <X \ leq b \} = \ int_a ^ bf (x) \) , called \ (f (x) \) is the continuous random variable \ (X-\) a probability density function.
The probability density function of two properties :
- \(f(x)\geq 0\)
- \(\int_{-\infty}^{+\infty}f(x)=1\)
- Continuous variables take the value of individual time with probability 0
Note:
- Interval of continuous random variable, not inclusive matter comprising
