Binomial Distribution Binomial probability distribution is defined as: * P(X=r) = nCr x pn x (1-p)n-r * Distribution is written as: X~B(n‚p) Conditions include: * Fixed number of trials * All trials are independent of one another * Probability of success remains constant * Each trial much have the same two possible outcomes E(X) = np Var(X) = npq [where q = 1 - p] SD(X) = Var (X) = npq To calculate the probabilities: * P(X ≤ x) = read off the
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modelling using Random Variables . . . . . . . . . . . . 2 Lecture 2. Random variables. Revision. 2.1 Random Variables and Their Distributions. General. . . . 2.2 Expected value= mean‚ Variance=( Standard Deviation)2 . 2.3 Common models. Specific Probability distributions. . . . . 2.4 Realization of Random Variables. Using Excel . . . . . . . 2.5 Expectation of a function of a random variable . . . . . . . 3 Lecture 3. Multivariate distributions. 3.1 Independence . . . . . . . . . . . . . . 3.2 Covariance
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Density is how compact particles are inside an object. Objects can be different sizes but have the same density because the density depends on how close particles are together‚ not the size of an object. The density of water is 1 g/㎤. Any object with a density less than that will float. Any object with density more than that will sink. Carbon dioxide‚ or CO2‚ also played a big role in this experiment. Many soft drinks contain CO2. Studies show that Sierra Mist had the most carbonation out of
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non-scattering‚ absorbing medium‚ the intensity of the light after passing though the medium is given by: (1) Where I(0) is the intensity at s=0‚ a is the absorption cross section of a single particle for radiation of wavelength ‚ n is the number density of the medium‚ and s is the length of the medium. We can apply the relationship to solar radiation passing though the atmosphere. From equation 1‚ we find that ‚ the transmissivity of the slant path of the atmosphere at a given wavelength is
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produced by a printer is normally distributed with a mean diameter of 0.005 cm and a standard deviation of 0.001 cm. i) What is the probability that the diameter of a dot exceeds 0.0065 cm? [2 marks] ii) What is the probability that a diameter is between 0.0035 and 0.0065 cm? [2 marks] iii) What standard deviation of diameters is needed so that the probability in part ( ii) is 0.995? [3 marks] c) A plastic casing for a magnetic disk is composed of two halves. The thickness of each half is
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properties: (1) (2) (3) (4) W0 = 0. With probability 1‚ the function t → Wt is continuous in t. The process {Wt }t≥0 has stationary‚ independent increments. The increment Wt+s − Ws has the N ORMAL(0‚ t) distribution. A Wiener process with initial value W0 = x is gotten by adding x to a standard Wiener process. As is customary in the land of Markov processes‚ the initial value x is indicated (when appropriate) by putting a superscript x on the probability and expectation operators. The term independent
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The Research Foundation of CFA Institute Literature Review Risk Management: A Review Sébastien Lleo‚ CFA Imperial College London The concept of risk has been central to the theory and practice of finance since Markowitz’s influential work nearly 60 years ago. Yet‚ risk management has only emerged as a field of independent study in the past 15 years. Advances in the science of risk measurement have been a main contributor to this remarkable development as new risk measures have been proposed
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Tab 1----All graphs‚ including the histogram should have an appropriate title and the x and y axis should be labeled. Bin and frequency does not give any information as to what is being represented by the numerical data in the histogram (hint: Electricity cost (in $) and one-bedroom apartments). As Professor Ellis stated in the lectures‚ graphs should be able to stand alone. “A Graph should sing its song!” Bin ranges are correct. However‚ the largest percentage does not lie between 139‚ 179. Both
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what is the probability that he/she b) has high blood pressure (event A)? c) has high level of cholesterol(event B)? d) has high blood pressure and high level of cholesterol (event A and B)? e) has either high blood pressure or high level of cholesterol (event A or B)? f) Use the above to check the probability formula: P(A or B) = P(A) + P(B) - P(A and B). 2. A committee of 5 people is to be formed randomly from a group of 10 women and 6 men. Find the probability that the committee
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+2 +3 X = N( ‚ 2 ) Determining Normal Probabilities Since each pair of values for and represents a different distribution‚ there are an infinite number of possible normal distributions. The number of statistical tables would be limitless if we wished to determine probabilities for all of them. The standard normal distribution z has a mean of 0 and a standard deviation of 1‚ i.e. z = N(0‚1)‚ and provides a basis for computing probabilities for all normal distributions. We must therefore
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