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The probability distribution whose frequency function f(x)= 1/n( x = x1, x2, …, xn) is known as
- a)Binomial distribution
- b)Poisson distribution
- c)Uniform distribution
- d)Normal distribution
Correct answer is option 'C'. Can you explain this answer?
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The probability distribution whose frequency function f(x)= 1/n( x = x...
Explanation:
The given probability distribution is defined by the frequency function f(x) = 1/n for x = x1, x2, ..., xn. This means that each value of x from x1 to xn has an equal probability of occurring, which is 1/n.
Uniform Distribution:
The probability distribution described above is known as the uniform distribution. In a uniform distribution, all values in the range of the distribution have an equal probability of occurring. This is often represented graphically as a rectangle, where each value in the range has the same height.
Properties of Uniform Distribution:
1. All values in the range have an equal probability of occurring.
2. The probability density function is constant within the range and zero outside the range.
3. The mean and variance of a uniform distribution can be calculated using the following formulas:
Mean = (a + b) / 2
Variance = (b - a)^2 / 12
Where a and b are the minimum and maximum values in the range, respectively.
Examples:
Some examples of situations that follow a uniform distribution include:
1. Rolling a fair die.
2. Choosing a random number between two given values.
3. Selecting a random point within a given area or volume.
4. Selecting a random time within a given time interval.
Conclusion:
In conclusion, the given probability distribution is an example of the uniform distribution, where all values in the range have an equal probability of occurring. This type of distribution is useful in many different applications, particularly when there is no reason to expect certain values to be more likely than others.
The given probability distribution is defined by the frequency function f(x) = 1/n for x = x1, x2, ..., xn. This means that each value of x from x1 to xn has an equal probability of occurring, which is 1/n.
Uniform Distribution:
The probability distribution described above is known as the uniform distribution. In a uniform distribution, all values in the range of the distribution have an equal probability of occurring. This is often represented graphically as a rectangle, where each value in the range has the same height.
Properties of Uniform Distribution:
1. All values in the range have an equal probability of occurring.
2. The probability density function is constant within the range and zero outside the range.
3. The mean and variance of a uniform distribution can be calculated using the following formulas:
Mean = (a + b) / 2
Variance = (b - a)^2 / 12
Where a and b are the minimum and maximum values in the range, respectively.
Examples:
Some examples of situations that follow a uniform distribution include:
1. Rolling a fair die.
2. Choosing a random number between two given values.
3. Selecting a random point within a given area or volume.
4. Selecting a random time within a given time interval.
Conclusion:
In conclusion, the given probability distribution is an example of the uniform distribution, where all values in the range have an equal probability of occurring. This type of distribution is useful in many different applications, particularly when there is no reason to expect certain values to be more likely than others.
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The probability distribution whose frequency function f(x)= 1/n( x = x1, x2, …, xn) is known asa)Binomial distributionb)Poisson distributionc)Uniform distributiond)Normal distributionCorrect answer is option 'C'. Can you explain this answer?
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