Question

What is the correct answer to question 11 please? A random variable \( \boldsymbol{x} \) follows continuous uniform distribution on the interval \( [14,30] \). Find the variance \( \operatorname{Var}(\mathrm{X}) \). Note: Enter your answer with 2 dec

Answer 1

The variance Var(X) for a continuous random variable X that follows a uniform distribution on the interval [14,30] is calculated using the formula (b - a)^2 / 12, which results in approximately 21.33 when rounded to two decimal places.

Step-by-step explanation:

The question asks to find the variance Var(X) for a continuous random variable X that follows a uniform distribution on the interval [14,30]. To calculate the variance of a uniform distribution between intervals a and b, we use the formula Var(X) = (b - a)^2 / 12. In this case, a equals 14 and b equals 30.

First, find the difference between b and a: 30 - 14 = 16.

Next, square this difference: 16^2 = 256.

Then, divide by 12 to get the variance: 256 / 12 ≈ 21.33.

The variance of X, Var(X), is approximately 21.33 (rounded to two decimal places).