Tag: statistics
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Normal Distribution
A random variable X is said to follow a Normal Distribution with parameters [katex] \mu [/katex] and [katex] \sigma [/katex] if it has a probability density function given by: A random variable X is said to follow a Normal Distribution with parameters [katex] \mu [/katex] and [katex] \sigma [/katex] if it has a distribution function…
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Monte Carlo Methods
A Monte Carlo method is a computational / numerical method that uses random numbers to compute / estimate a quantity of interest. The quantity of interests may be the mean of a random variable , functions of several means , distributions of random variables or high dimensional integrals. Basically, Monte Carlo methods may be grouped…
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STB – 2019
Consider a count variable X following a Poisson distribution with parameter θ > 0, where zero count (i.e., X = 0) is not observable. We have n observations X1, . . . , Xn from this distribution. Let denote the sample mean. a) Derive the quantity for which is an unbiased estimator. b) Suppose that the observed value…
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Ratio Estimation
INTRODUCTION: In Survey Sampling, we often use information on some auxiliary variable, to improve our estimator of the finite population parameter, by giving our estimator protection against selection of bad sample. One such estimator is the ratio estimator introduced as follows: In practice, we are often interested to estimate the ratio of the type: For…
Discovering Statistics 