Tiêu đề 1) Statistics Sum-up.pdf ✅

Chapter 1 Correlation Degrees of correlation weak: If 0 < r q 0.4 or -0.4 q r < 0 moderate (middling): If 0.4 < r q 0.6 or -0.6 q r < -0.4 strong: If 0.6 < r < 1 or -1 < r < -0.6 Pearson’s linear correlation coefficient: r = n ∑ xy − ∑ x × ∑ y √n ∑ x 2 − (∑ x) 2√n ∑ y 2 − (∑ y) 2 Spearman’s rank correlation coefficient: r = 1 − 6 ∑ D 2 n(n2 − 1) Regression y = a + bx Where: a is the length of y-intercept b is the regression coefficient of y on x and it expresses the slope of the regression line on the positive direction of x-axis. b = n ∑ xy − ∑ x × ∑ y n ∑ x 2 − (∑ x) 2 , a = ∑ y − b ∑ x n The regression line equation is used for : Predicting the value of y if the value of x is known, Identifying the error can be determined by the relation : Error = | Table value − value satisfying the regression equation | (No correlation) (Nihilistic correlation) using calculator : https://youtu.be/wqH4g-bjmOs
Chapter 2 Remember for every random event A ⊂ S there exists a real P(A) where : Number of elements of A P(A) = Number of elements of S The probability that A occurs 0 ≤ P(A) ≤ 1 The probability that A does not occur P(A`)= 1 − P(A) The prob. of occurrence of A or B (at least one of them) P(A ∪ B) = P(A) + P(B) − P(A ∩ B) The prob. of occurrence of A and B (together) P(A ∩ B) = P(A) + P(B) − P(A ∪ B) The prob. of A only P(A − B) = P(A) − P(A ∩ B) The prob. of non-occurrence of A and B (neither A nor B) P(A` ∩ B`) = 1 − P(A ∪ B) The prob. of non-occurrence of one of them at most P(A` ∪ B`) = 1 − P(A ∩ B) The prob. of A or non-occurrence of B P(A ∪ B`) = 1 − P(B) + P(A ∩ B) If P(A) = P(A`) P(A) = 1⁄2 , P(A`) = 1⁄2 P(S) = 1 , P(imposible event) = P() = 0 If A , B are two mutually exclusive events of S , then: P(A∩B) = P() = 0 Conditional probability: If S is the sample space of a random experiment and A and B are two events of this space, then, the probability of occurring the event A in condition of occurring the event B and it is denoted by the symbol P(A|B) and read as the probability of occurring event A in condition of occurring event B. it can be determined by the next relation: P(A|B) = P(A ∩ B) P(B) where P(B) > 0 Notice that: the conditional probability has the same properties of the unconditional one. 0 ≤ P(A|B) ≤ 1 , P(A|B) ≠ P(B|A) , P(S|B) = P(S∩B) P(B) = P(B) P(B) = 1 The two independent events: It is said that A and B are two independent events if and only if P(A ∩ B) = P(A) × P(B) It is noticed that if the two events A , B are independent and P(B) 0 then P(A|B) = P(A) i.e. the occurrence of an event doesn’t affect the occurrence of the other event. Dependent events: A and B are two dependent events if P(A ∩ B) ≠ P(A) × P(B)
illustration video : https://youtu.be/MnlonJ_J2wU
Chapter 3 Random Variable Any function X: S → R is called a random variable and the values, which the random variable takes, is called the range of the random variable. Types of Random Variable 1. Discrete: Its range is a finite set. (i.e. it can be counted) of the set of real numbers. 2. Continuous: its range is an interval of the real numbers (closed or opened) i.e. it is a non-counted set of real numbers. Probability distribution function of the discrete random variable: ∑f(Xi ) n i=1 = 1 Continuous random variable: To find P(a < x < b) we find the area under the curve f(x) = {Rule, a < x < b 0, otherwise P(a < x < b) = f(a) + f(b) 2 × (b − a) If f(x) is Probability Density Function P(a < x < b) = 1 Mean (expectation): μ = ∑Xi f(Xi ) n i=1 Variance: σ 2 = ∑Xi 2 f(Xi ) n i=1 − μ 2 Standard Deviation: σ = √σ 2 Coefficient of Variation: σ μ × 100% xi x1 x2 x3 ...... xn f (xi) f (x1) f (x2) f (x3) ...... f (xn) using calculator : https://youtu.be/wqH4g-bjmOs