Final answer:
To calculate the mean of a discrete probability distribution, use the formula μ = Σ xP(x). To find the standard deviation, calculate the variance with σ² = Σ (x − μ)² P(x), and then take the square root of the variance. For certain distributions, shortcut formulas exist.
Step-by-step explanation:
Calculating Mean and Standard Deviation of a Discrete Probability Distribution
To calculate the mean (μ) of a discrete probability distribution, you would use the formula μ = E(X) = Σ xP(x), where x is a value of the random variable and P(x) is the probability associated with that value. You need to make sure to multiply each value of the random variable by its corresponding probability and then add all these products together.
To calculate the standard deviation (σ) of a probability distribution, you should find the variance first using the formula σ² = Σ (x − μ)² P(x), and then take the square root of the variance. This requires squaring each deviation from the mean, multiplying by the respective probability, and then summing all these products before finally taking the square root to get the standard deviation.
For some specific types of distributions, like the geometric distribution, there are shortcut formulas to calculate these parameters, such as μ = 1/p and σ² = (1 - p)/p² for a geometric distribution with success probability p. However, for many probability distributions, these calculations often require the use of a calculator or computer software to minimize rounding errors.