Question

you investigate the number of earthquakes that occur in a year. you get the following outcomes: what is the variance of this random phenomenon?

Answer 1

Based on the given information, the variance of this random phenomenon is 0.1051.

How to calculate the variance of a random phenomenon

To calculate the variance of a random phenomenon, compute the weighted average of the squared deviations from the mean.

Here's how you can calculate the variance for the given outcomes:

Calculate the mean:

Mean (μ) = (Number of earthquakes * Probability)

= (0 * 0.95) + (1 * 0.03) + (2 * 0.02)

= 0.03 + 0.04

= 0.07

Calculate the squared deviations from the mean for each outcome:

Squared deviation = (Number of earthquakes - Mean
`)^2`

For 0 earthquakes:

Squared deviation =
`(0 - 0.07)^2` = 0.0049

For 1 earthquake:

Squared deviation =
`(1 - 0.07)^2` = 0.8649

For 2 earthquakes:

Squared deviation =
`(2 - 0.07)^2` = 3.7249

Calculate the weighted average of the squared deviations:

Variance = (Squared deviation * Probability)

Variance = (0.0049 * 0.95) + (0.8649 * 0.03) + (3.7249 * 0.02)

= 0.004655 + 0.025947 + 0.074498

= 0.1051

Therefore, the variance of this random phenomenon is 0.1051.

you investigate the number of earthquakes that occur in a year. you get the following outcomes:

Number of earthquakes: 0, 1, 2

Probability: 0.95, 0.03, 0.02

what is the variance of this random phenomenon?