How To Calculate Range of Values Of A Random Variable (Binomially Distributed)

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  • #1
moonman239
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1 Calculate the expected value of variable x (or E(x)) (number of trials * probability of success)
2 Calculate the variance (expected value * probability of a failure)

Take everything to the right of the decimal in the variance off. Then the range of future values is E(x) plus/minus the variance.
 
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  • #2
The probability of error will always be below .5.
 
  • #3
Are you asking whether this is true? On what basis do you make these statements?
 

1. What is a binomially distributed random variable?

A binomially distributed random variable is a type of discrete probability distribution that represents the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes (usually referred to as "success" and "failure"). It is often used to model real-world situations such as coin flips or the success rate of a medical treatment.

2. How do I calculate the range of values for a binomially distributed random variable?

The range of values for a binomially distributed random variable is dependent on the number of trials and the probability of success for each trial. To calculate the range, you can use the formula: Range = Number of trials * Probability of success. For example, if you have 10 trials with a probability of success of 0.5, the range would be 10 * 0.5 = 5.

3. What is the significance of calculating the range of values for a binomially distributed random variable?

Calculating the range of values for a binomially distributed random variable can help you understand the possible outcomes of a given situation and the likelihood of each outcome occurring. It can also help you make informed decisions and predictions based on the data.

4. Can the range of values for a binomially distributed random variable be negative?

No, the range of values for a binomially distributed random variable cannot be negative. This is because the number of trials and the probability of success are always positive values, and multiplying them will result in a positive range.

5. How does the shape of a binomial distribution change as the number of trials increases?

As the number of trials increases, the shape of a binomial distribution becomes more symmetrical and bell-shaped. This is because the more trials there are, the closer the distribution will resemble a normal distribution. This phenomenon is known as the central limit theorem.

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