Sampling

Sample and Sampling Procedure ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Randomness in Sampling ,[object Object],[object Object],[object Object]

Random sampling ,[object Object],[object Object]

Sampling Distribution ,[object Object],[object Object],[object Object]

Example ,[object Object],[object Object],[object Object],[object Object]

Sampling Distribution Mean ,[object Object],[object Object],[object Object]

Sampling Distribution of the sample mean ,[object Object],Of these observations is called the sample mean. We need to consider the sampling distribution of the random variable X.

Variance of Sampling Distribution of Means ,[object Object],[object Object],[object Object]

Sampling mean distribution from a normal population ,[object Object],Moreover, by Central Limit theorem, even if the population distribution is not normal, but the sample size is moderately large, then the distribution of X, will still be very close to normal.

Examples-1 and 2. ,[object Object],[object Object]

Sample Proportion Distribution ,[object Object],[object Object]

Sampling distribution of the Sample proportion.

[object Object],[object Object]

Sampling distribution of the sample variance ,[object Object],Is called the sample variance. Its square root is called the sample standard deviation

Chi-Square Distribution ,[object Object],The mean and variance of  2 distribution are equal to the number of degrees of freedom and twice the number of degrees of freedom respectively .

Sampling distribution of the sample variance ,[object Object]

Sampling

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Sampling