Determine whether or not the function is a probability density function over the given interval. \[ f(x)=\frac{1}{4} x,[3,6] \] Yes No

Step 1 ：We are given the function \(f(x)=\frac{1}{4} x\) over the interval [3,6] and asked to determine whether it is a probability density function (pdf).

Step 2 ：A function is a pdf if it satisfies two conditions: (1) The function must be non-negative for all x in the given interval. (2) The integral of the function over the entire space must equal to 1.

Step 3 ：In this case, the function is non-negative for all x in the interval [3,6]. So, the first condition is satisfied.

Step 4 ：Now, we need to check the second condition. We need to integrate the function over the interval [3,6] and check if the result is 1.

Step 5 ：The integral of the function over the interval [3,6] is 3.375, which is not equal to 1. Therefore, the function does not satisfy the second condition to be a probability density function.

Step 6 ：\(\boxed{\text{No, the function is not a probability density function over the given interval.}}\)