box contains prize. (b) Explain the rolling of a fair die and then flipping of a fair coin with the help of tree diagram. Q.2 (a) How can we differentiate between continuous and discrete random variables. Explain with the help of examples. (b) Let X be a random variable having normal distribution with mean 48 and standard deviation 10. Then find [pic]. Q.3 (a) Compute the mean‚ median‚ mode and standard deviation for the following discrete probability distribution.
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is a sequence {x1‚ x2‚ ...‚ xT } or {xt} ‚ t = 1‚ ...‚ T‚ where t is an index denoting the period in time in which x occurs. We shall treat xt as a random variable; hence‚ a time-series is a sequence of random variables ordered in time. Such a sequence is known as a stochastic process. The probability structure of a sequence of random variables is determined by the joint distribution of a stochastic process. A possible probability model for such a joint distribution is: xt = α +
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outcome q=1-p is the probability that the outcome is a failure If X is a random variable denoting the number of successful outcome‚ the probability function of X is given P X r nCr p r q nr Where q=1-p r=0‚1‚2‚3‚….. X~B(n‚p) The n trials and probability of success p are called the parameters of the binomial distribution Binomial distribution consists of a number of successive trials of a random experiment. Each trial has only 2 outcome (success & failure) Mean and
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Normal Distribution:- A continuous random variable X is a normal distribution with the parameters mean and variance then the probability function can be written as f(x) = - < x < ‚ - < μ < ‚ σ > 0. When σ2 = 1‚ μ = 0 is called as standard normal. Normal distribution problems and solutions – Formulas: X < μ = 0.5 – Z X > μ = 0.5 + Z X = μ = 0.5 where‚ μ = mean σ = standard deviation X = normal random variable Normal Distribution Problems and Solutions – Example
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conclusions from data that are subject to random variation‚ for example‚ observational errors or sampling variation. Initial requirements of such a system of procedures for inference and induction are that the system should produce reasonable answers when applied to well-defined situations and that it should be general enough to be applied across a range of situations. Inferential statistics are used to test hypotheses and make estimations using sample data. Variable (mathematics)‚ a symbol that represents
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Omkar & Yaying Wednesday 5-6pm WEEK 3 BES PASS Descriptive Statistics Population - a set of all possible observations. Sample - a portion of a population. We often use information concerning a sample to make an inference (conclusion) about the population. Parameter - describes a characteristic of the population‚ eg: the population variance Statistic- describes a characteristic of a sample‚ eg: the sample variance Frequency Distribution and Histograms Class - a collection of
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Vice President of Marketing for Dysk Compyer‚ Inc must decide whether to introduce a mid-priced 2 version of the firm’s DC6900 minicomputer product line-the DC6900-X minicomputer. The DC6900-X would sell for $ 3900‚ 3 with unit variable costs of $ 1‚800. Projections made by an independent marketing research firm indicate that the DC6900-X 4 would achieve a sales volume of 500‚000 units next year‚ in its first year of commercialization. One-half of the first year’s
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=STDV() =RANDINV() =VLOOKUP() and few more . These are widely used function when I simulated data in excel. In task 1 I find out how to calculate or forecast how much card should we print. I use a random variable with =RAND( function and use =VLOOKUP() function to find out demand from discreet variable called cumulative probabilities. This is discrete because we find out the range by frequency distribution. Then I use if function to calculate disposable cost with =IF (Demand>Production‚(Demand-Production)*Disposable
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¡ P.1 Random Variables ¡ P.2 Probability Distributions ¡ P.3 Joint‚ Marginal and Conditional Distributions ¡ P.4 A Digression: Summation Notation ¡ P.5 Properties of Probability Distributions ¡ P.6 The Normal Distribution Principles of Econometrics‚ 4th Edition Probability Primer Page 3 1 1/08/13 P.1 Random Variables Principles of Econometrics‚ 4th Edition Probability Primer Page 4 P.1 Random Variables ! A random variable is a variable
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An additive noise is characteristic of almost all communication systems. This additive noise typically arises from thermal noise generated by random motion of electrons in the conductors comprising the receiver. In a communication system the thermal noise having the greatest effect on system performance is generated at and before the first stage of amplification. This point in a communication system is where the desired signal takes the lowest power level and consequently the thermal noise
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