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29 Φεβ 2024 · A possible pdf for X is given by. f(x) = {x, for 0 ≤ x ≤ 1 2 − x, for 1 <x ≤ 2 0, otherwise. The graph of f is given below, and we verify that f satisfies the first three conditions in Definition 4.1.1: From the graph, it is clear that f(x) ≥ 0 f (x) ≥ 0. , for all x ∈ R x ∈ R.
1 ••• Master List of Formulas Chapter 1 IntroduCtIon and desCrIptIve statIstICs NONE. Chapter 2 FrequenCy dIstrIbutIons In tables and Graphs Σx (Frequency) Σx n (Relative frequency) Σx n × 100 (Relative percent) Chapter 3 summarIzInG data: Center tendenCy µ= Σx N (Population mean) M = Σx n (Sample mean) M Mn w n = Σ × Σ (Weighted sample mean) Chapter 4 summarIzInG data: varIabIlIty
INTRODUCTION TO STATISTICAL ANALYSIS. LEARNING OBJECTIVES: After studying this chapter, a student should understand: notation used in statistics; how to represent variables in a mathematical form for statistical purposes; how to construct frequency distributions, histograms, and bar graphs;
2 2 12 2 22 1 11 2 2 2 2 2 1 2 2 2 12 2 12 Confidence Interval for and 11 Hypothesis Test Statistic: where numerator . . 1 and denominator . . 1 right left ss ss FF s F ss s df n df n σ σ σ σ • << • =≥ =−= −
Conditional probability formula: P(A⋂B) P (A|B) = P(B) Chebychev’s rule: ( 1 − 1. k 2 ) Multiplicative Rule of Probability: P (A ⋂ B ) = P (B) × P (A|B) Sample z-score formula: . z = x−x. s. Multiplicative Rule of Probability of events are independent: P (A ⋂ B ) = P (A) × P (B) Discrete - Continuous - Probability - Other.
Statistics and their sampling distributions. Our data set is a realization of a sample (random vector) X from an unknown population P Statistic T (X): A measurable function T of X; T (X) is a known value whenever X is known. Statistical analyses are based on various statistics.
Definition of Expectation. = E(X ) Def: Mean aka. Expected value. Let X be a random variable with p(d)f f (x). The mean, or expected value of X, denoted E(X), is defined as follows. discrete: X E(X) = xf(x) All x. assuming the sum exists. continuous: 1. E(X) = xf(x) dx. 1. assuming the integral exists.
