Table of Contents

- 1 What are independent random samples?
- 2 Which of the following are required for an independent random sampling?
- 3 What is the probability that the first student selected will be a female?
- 4 What are the two requirements for a random sample?
- 5 Are two events independent?
- 6 What are the requirements that must be satisfied for a sample to be random?

## What are independent random samples?

The samples that are selected randomly from the population are known as random samples. Independent random samples are selected by randomization of each sampling element. An independent random sample is a sequence of observations which are not dependent on any other sample or data.

### Which of the following are required for an independent random sampling?

Sampling must be done without replacement. Every time an individual is selected for the sample, each of the remaining individuals has a higher chance of being included. Sampling must be done with replacement.

**How do you know if an B is independent?**

Events A and B are independent if the equation P(A∩B) = P(A) · P(B) holds true. You can use the equation to check if events are independent; multiply the probabilities of the two events together to see if they equal the probability of them both happening together.

**What random variable is independent?**

An independent random variable is a random variable that doesn’t have an effect on the other random variables in your experiment. In other words, it doesn’t affect the probability of another event happening. The opposite is a dependent random variable, which does affect probabilities of other random variables.

## What is the probability that the first student selected will be a female?

1 Expert Answer There are 28 + 52 or 80 total members in the class so the probability that a randomly selected person will be a female is 52/80 or (reduced) 13/20.

### What are the two requirements for a random sample?

Each individual in the population has an equal chance of being selected. 2. If more than one individual is to be selected for the sample, there must beconstant probability for each and every selection.

**How do you prove independence?**

**What is P A or B if A and B are independent?**

Formula for the probability of A and B (independent events): p(A and B) = p(A) * p(B). If the probability of one event doesn’t affect the other, you have an independent event. All you do is multiply the probability of one by the probability of another.

## Are two events independent?

Two events are independent if the result of the second event is not affected by the result of the first event. If A and B are independent events, the probability of both events occurring is the product of the probabilities of the individual events.

### What are the requirements that must be satisfied for a sample to be random?

**What are the requirements for a simple random sample?**

A simple random sample takes a small, random portion of the entire population to represent the entire data set, where each member has an equal probability of being chosen. Researchers can create a simple random sample using methods like lotteries or random draws.

**What is PA and B?**

Conditional probability: p(A|B) is the probability of event A occurring, given that event B occurs. Joint probability: p(A and B). The probability of event A and event B occurring. It is the probability of the intersection of two or more events. The probability of the intersection of A and B may be written p(A ∩ B).