Question

Calculate the mean, variance, and standard deviation of the following discrete probability distribution.

Answer 1

To find the mean, variance, and standard deviation of a discrete probability distribution, you multiply each value of the random variable by its probability, sum these for mean, compute squared deviations times probabilities for variance, and take the square root of variance for standard deviation.

Step-by-step explanation:

To calculate the mean, variance, and standard deviation of a discrete probability distribution, we follow certain formulas. The mean (or expected value) μ of a discrete random variable X is the long-term average outcome of a statistical experiment. The variance (σ²) is a measure of how spread out the values of X are around the mean. The standard deviation (σ) is the square root of the variance and indicates the average distance from the mean.

The mean is calculated as:

• μ = Σ (x × P(x))

Where x represents the possible values of the random variable, and P(x) is the probability of each value occurring.

The variance is calculated as:

• σ² = Σ ((x − μ)² × P(x))

And for the standard deviation:

• σ = √σ²

To calculate these, one must follow these steps:

1. Identify all possible values of the random variable X.
2. Compute the probability of each value (P(x)).
3. Calculate the mean by multiplying each value by its probability, and then summing all products.
4. For each value, find the difference from the mean, square it, multiply by the probability, and sum all these products to get the variance.
5. Take the square root of the variance to find the standard deviation.