Question

Suppose X has a continuous uniform distribution over the interval [-1,1].

Round your answers to 3 decimal places.
(a) Determine the mean, variance, and standard deviation of X.

Answer 1

The mean of X is 0, the variance is 1/3, and the standard deviation is approximately 0.577.

Step-by-step explanation:

(a) Mean:

The mean of a continuous uniform distribution is the average of the endpoints of the interval.

The mean of X is the average of -1 and 1:

Mean = (-1 + 1) / 2 = 0

(b) Variance:

The variance of a continuous uniform distribution is calculated using the formula:

Variance = (b - a)^2 / 12

where 'a' and 'b' are the endpoints of the interval.

The variance of X is:

Variance = (-1 - 1)^2 / 12 = 1/3

(c) Standard Deviation:

The standard deviation of a continuous uniform distribution is the square root of the variance.

The standard deviation of X is:

Standard Deviation = sqrt(1/3) ≈ 0.577