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Probability & Statistics for Machine Learning & Data Science (25) Confidence Intervals and Hypothesis testingHypothesis Testingt-DistributionWhen the data can be modeled as a Gaussian distribution with parameters $\mu$ and $\sigma^2$, the sample mean will also follow a Gaussian distribution of the same mean, but with a smaller standard deviation.If we don’t know the standard deviation, then we use T-statistics instead of Z-statistics.But using T-statistics doe.. 더보기
Probability & Statistics for Machine Learning & Data Science (24) Confidence Intervals and Hypothesis testingHypothesis TestingDefining HypothesesThe null hypothesis is when nothing is happening.The alternative hypothesis is when something is happening and something we want to prove using the data.Rejecting the alternative hypothesis means we don’t have enough evidence, but it doesn’t mean we accept the null hypothesis.We are simply rejecting the hypothesis an.. 더보기
Probability & Statistics for Machine Learning & Data Science (23) Confidence Intervals and Hypothesis testingQuizQ1Consider two sets of samples drawn from the same population that are randomly selected. Set X has a sample size = 10, and set Y has a sample size = 100. Which of the following statements is accurate about the confidence interval for the mean of the samples?The confidence interval for set X is larger than the confidence interval for set Y.The confi.. 더보기
Probability & Statistics for Machine Learning & Data Science (22) Confidence Intervals and Hypothesis testingConfidence IntervalsDifference Between Confidence and ProbabilityConfidence used here is not a probability.The population mean is unknown and fixed, not a random value.Confidence level is the rate of success vs failure when constructing the confidence interval.Unknown Standard DeviationWhen we know the population standard deviation, we can generate a no.. 더보기
Probability & Statistics for Machine Learning & Data Science (21) Confidence Intervals and Hypothesis testingThis week you will learn another estimation method called interval estimation. The most common interval estimates are confidence intervals; you will see how they are calculated and how to interpret them correctly. In lesson 2, you will learn about hypothesis testing where estimates are formulated as a hypothesis and then tested in the presence of availa.. 더보기
Probability & Statistics for Machine Learning & Data Science (20) Sampling and Point estimationPoint EstimationBack to "Bayesics”Although an event could generate the highest probability (maximum likelihood), if the event itself is unlikely, we wouldn’t choose it.So conditional probability solely is not something we want to maximize, instead, we want to maximize the probability of two events happening at the same time, which is $P(A \cap B) = P(A|B)P(B)$ and th.. 더보기
Probability & Statistics for Machine Learning & Data Science (19) Sampling and Point estimationPoint EstimationPoint EstimationThe most common point estimation method is maximum likelihood estimation (MLE), which is very popular in machine learning.MLE can be generalized using Bayes’ theorem to a Bayesian version of a point estimator called the maximum a posteriori estimation.MAP or maximum a posteriori estimation can be thought of as a maximum likelihood esti.. 더보기
Probability & Statistics for Machine Learning & Data Science (18) Sampling and Point estimationQuizQ1Consider the following population, P, where P = {1, 1, 3, 5, 10}And the following sample, S, where S = {1, 3}What is the value of the sample mean?26It cannot be computed with the given information4Answer더보기1The sample mean should be calculated from the sample set’s numbers only. Therefore, the sample mean is (1+3)/2 = 2Q2What is the difference between a sample .. 더보기
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