Question

Sampling distribution question

1. State the definition of sampling distribution?
2. Let’s assume that we have a Bernoulli random variable X,

X = a with probability 0.78,

X = b with probability 0.22,  

Where a and b are the third and fourth digit of your student number, respectively.(a=9,b=9) Develop a sampling distribution for sample means of the Bernoulli distribution when the sample size is 6

3. What is the expected value of sample means in question 3.b? What is the variance of the sample means?
4. If the sample size increases to a large number n (n is greater than 30), how are the sample means distributed?

Answer 1

a) In statistics, a sampling distribution or finite-sample distribution is the probability distribution of a given random-sample-based statistic. If an arbitrarily large number of samples, each involving multiple observations (data points), were separately used in order to compute one value of a statistic (such as for example, the sample mean or sample variance) for each sample, then the sampling distribution is the probability distribution of the values that the statistic takes on. In many contexts, only one sample is observed, but the sampling distribution can be found theoretically.