Question

consider the given uniform density curve. what is the value of the mean? 4.25 4.5 4.75 5

Explanation:

Step1: Recall the formula for the mean of a uniform distribution

For a uniform distribution \(X\sim U(a,b)\), the mean \(\mu=\frac{a + b}{2}\).

Step2: Identify \(a\) and \(b\) values

From the given uniform density curve, \(a = 3\) and \(b=6\).

Step3: Calculate the mean

Substitute \(a = 3\) and \(b = 6\) into the formula \(\mu=\frac{3+6}{2}=\frac{9}{2}=4.5\)

Answer:

\(4.5\)