Q.12. What is the Poisson distribution?
Ans. Poisson distribution is a discrete probability distribution. It is used in such cases where the value of his is very large Since in these cases binomial distribution does not give appropriate theoretical frequencies, Poisson distribution is found very appropriate. It is worth mentioning that Poisson distribution is a limiting form of binomial distribution as n moves towards infinity and p moves towards zero but np or mean remains constant and finite. Poisson distribution is used to describe the behavior of rare events such as the number of germs in one drop of pure water, number of printing errors per page, number of telephone calls arriving per minute at a telephone switchboard, etc.
Q.13. Write the four uses of Poisson distribution.
Ans. The four uses of Poisson distribution are:
- In insurance problems to count the number of casualties.
- In biology to count the number of bacteria.
- In counting the number of defects per item in statistical quality control.
- A number of accidents take place per day on a busy road.
Q.14. Describe the meaning of normal distribution.
Ans. The normal distribution is a continuous probability distribution in which the relative frequencies of a continuous variable are distributed according to normal probability law. In simple words, it is symmetrical distribution in which the frequencies are distributed evenly about the mean of the distribution
Q.15. Describe the four main properties of normal distribution.
Ans. The four main properties of the normal distribution are
- Continuous distribution,
- Equality of central value,
- Equal distance of quartiles from the median.
Q.16. Give any three importance of theoretical frequency distribution.
Ans. The three importance of theoretical frequency distribution are as follows:
- Forecasting: Theoretical frequency distribution provides a base for prediction, projection, and forecasting.
- Substitute of Actual Data: They can be used as substitutes for actual distribution when obtaining the latter is costly or cannot be obtained at all.
- Test of Sampling: Theoretical frequency distributions serve as benchmarks against which to compare the actual frequency distributions and to find out whether the difference is significant or is merely due to fluctuations of sampling.
Q.17. What are the three main characteristics of the binomial distribution?
Ans. The three main characteristics of the binomial distribution are:
- Theoretical Frequency Distribution: Binomial distribution is a theoretical frequency distribution based on the Bernoulli theorem of algebra.
- Discrete Probability Distribution: The binomial distribution is a discrete probability distribution in which the number of successes 0, 1, 2, 3,…,n are given in whole numbers and not infractions.
- Presentation by Line Graph: The binomial distribution can also be presented graphically by means of a line graph, in which the number of successes is taken on X-axis and the probability of success is shown on Y-axis. For example, if a coin is tossed, then the probability of head or tail will be 1/2. If the coin is tossed twice, the probability of getting heads will be as follows: P (one head) = 2/4 = 1/2 and P(two heads) = 1/4
- Main Parameters: p and q are two main parameters of the binomial distribution and the entire distribution can be obtained with the help of these parameters.