1. Define Population, sample, parameter and estimator with examples. 2. Define variable. Distinguish between discrete variable and continuous variable. What do you mean by data? 3. Suppose there are 60 students in your class. We want to find the average height of these 60 students. Each student of this class will be our experimental unit. The characteristic of interest is height. If we collect numerical information on the height of all the students, then the collection of heights of 60 students will be the population data or the population of height. The average height of these 60 students say 5.7 feet. Then u=5.7 feet is our parameter. Suppose it is not possible to get the population data. In that case, we shall take a (random) sample of 10 students to estimate the average height of all students of the class. The collection of the heights of 10 students will be the sample data or sample. Suppose the average height of these 10 students is 5.6 feet. Then the sample mean x=5.6 feet is a statistic and value is used as an estimate of the population men H. Note that the size of a population (or population size) is the number of observations or experimental units in it. It is usually denoted by N. And the size of a sample (or sample size) is the number of observations or experimental units in it. It is usually denoted by n. Answer the follwing questions: 1. What is the population data? N=? 2. µ =5.7. Why is this a parameter? 3. What is the sample data? n=? 4. Why is sample data used instead of population data? 5. x is a statistic. Why? 6. x is an estimator. Why? 7. What is the experimental unit? 8. What is the variable being measured? 9. Is the variable qualitative or quantitative? 10. Is the variable discrete or continuous?
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
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