Question
Download Solution PDFIf random variable X follows binomial distribution with parameter n and p with mean 15 and variance 10, then the value of mode is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFThe correct answer is 46/3.
Key Points
- The mode of a binomial distribution is the value of x that has the highest probability of occurrence.
- In a binomial distribution with parameters n and p, the mode can be found using the formula: mode = floor(n * p), where "floor" represents the greatest integer less than or equal to the argument.
- The mean and variance of a binomial distribution can be used to find the values of n and p, and subsequently the mode.
- The mode, mean and variance are important characteristics of a distribution that describe the shape, central tendency and spread of the data.
- Understanding the properties of binomial distribution and how to find the mode, mean and variance is important in many areas of statistics and data analysis.
Additional Information
- The mode of a binomial distribution is the value of x that has the highest probability of occurrence.
- In a binomial distribution with parameters n and p, the mode can be found using the formula:
- mode = floor(n * p)
- Where "floor" represents the greatest integer less than or equal to the argument.
- Given that the mean of the distribution is 15 and the variance is 10, we can find n and p by solving two equations.
- The mean of a binomial distribution is equal to n * p, and the variance is equal to n * p * (1 - p).
- Solving for n and p and substituting into the formula for the mode, we get 46/3 as the answer.
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