References: 1. Y. S. Chao and H. Teicher‚ Probability Theory. Independence‚ Interchangeability‚ Martingale (Springer‚ New York‚ 1997). 3. N. Etemadi‚ An elementary proof of the strong law of large numbers‚ Z. Wahrsch. Verw. Gebiete 55 (1)‚ 119 (1981). indexed random variables‚ J. Multivariate Anal. 86
Premium Probability theory Random variable
University of Phoenix Material Learning Team Summary Worksheet TWO (due week Five) Brenda Rivera As a learning team‚ complete the table with formulas‚ rules‚ and examples from each section of Chapters 4‚ 5‚ 6‚7‚8‚9‚10 and 11 in the textbook. The completed summary will help prepare you for the Final Exam in Week 5. Points will be awarded for completion of the project. Study Table for Weeks One and Two Chapter 4 Systems of Linear Equations; Matrices (Section 4-1 to 4-6)
Premium Random variable Probability theory
Shridharan PRACTICE PROBLEMS 1. (a) What is the probability that a leap year selected at random will contain 53 Tuesdays? (b) What is the probability that a leap year selected at random will contain 53 Sundays or 53 Mondays? 2. A bag contains 8 black‚ 3 red and 9 white balls. If 3 balls are drawn at random ‚ find the probability that (a) all are black‚ (b) 2 are black and 1 is white‚ (c) 1 of each colour‚ (d)
Premium Normal distribution Probability theory Standard deviation
Four-D? In other words‚ what is the likelihood (probability) that the PDQ test score of a drive tested at DataStor will fall below 6.2? The probability that a PDQ test score of a drive tested at DataStor will fall below 6.2 is .38%. We arrived at this conclusion based on DataStor’s “in control” standard: Mean = 7.0 Std Dev = .3 Coincidentally‚ the mean and the X-bar of the data sample are the same‚ 7.0 (6.96). Using Normal Probabilities feature in PhStat‚ we determined:
Premium Standard deviation Probability theory Arithmetic mean
Continuous Distributions Distribution Uniform Normal Exponential Gamma Chi-square Beta Probability Function f (y) = f (y) = 1 ; θ ≤ y ≤ θ2 θ2 − θ1 1 1 1 (y − µ)2 √ exp − 2 2σ σ 2π −∞ < y < +∞ f (y) = 1 y α−1 e−y/β ; (α)β α 0<y<∞ f (y) = f (y) = f (y) = 1 −y/β e ; β>0 β 0<y<∞ (y)(v/2)−1 e−y/2 2v/2 (v/2) y2 > 0 ; (α + β) y α−1 (1 − y)β−1 ; (α) (β) 0<y<1 MomentGenerating Function Mean Variance θ1 + θ2 2 (θ2 − θ1 )2 12 µ σ2 β β2 (1 − βt)−1 αβ αβ 2 (1 − βt)−α v 2v
Premium Normal distribution Probability theory
– a) What is the probability of finding oil at all three of the sites? The table below shows the different events and there probabilities Event Symbol Probability The event of finding oil at 1st site A 0.70 The event of finding oil at 2nd site B 0.85 The event of finding oil at 3rd site C 0.80 Since all three events are independent and does not affect the outcome of the other so the probability of finding oil at all
Premium Rate of return HIV Investment
Economic growth Probability With Expansion Without Expansion High 0.20 S$ 65 million S$55 million Normal 0.55 S$ 8 million S$ 8 million Low 0.25 S$ 34 million S$ 30 million 1. What is the expected value of the Company with and without expansion? a b a x b Probability Without Expansion 0.20 S$55 million S$ 11 million 0.55 S$ 8 million S$ 4.4 million 0.25 S$ 30 million S$ 7.5 million S$ 22.9 million a b a x b Probability With Expansion 0.20 S$ 65 million S$ 13 million
Premium Finance Stock Stock market
Chapter 5 Measures of Central Tendency: Introduction A measure of central tendency is a single value that attempts to describe a set of data by identifying the central position within that set of data. As such‚ measures of central tendency are sometimes called measures of central location. They are also classed as summary statistics. The mean (often called the average) is most likely the measure of central tendency that you are most familiar with‚ but there are others‚ such as the median and the
Premium Standard deviation Arithmetic mean Median
Week 1 quiz Week 1‚ Quiz 1 Points Received 40/40 (100%) 1. Total cost equal the fixed cost plus the variable cost per unit divided by volume • True • False 2. Objective probabilities that can be stated prior to the occurrence of an event are • Subjective • A priori • Classical or a priori • None of the above 3. An experiment is an activity that results in one of several possible outcomes. • True
Premium Probability theory Economics Mathematics
random: | (a) | What is the probability all four of the selected homes have a security system? (Round your answer to 4 decimal places.) | Probability | | (b) | What is the probability none of the four selected homes have a security system? (Round your answer to 4 decimal places.) | Probability | | (c) | What is the probability at least one of the selected homes has a security system? (Round your answer to 4 decimal places.) | Probability | | (d) | Are the events
Premium Poisson distribution Binomial distribution Normal distribution