Find the value of the constant k so that the function is a probability density function in the indicated interval.
B)
C)
D)
E)

Question

Find the value of the constant k so that the function is a probability density function in the indicated interval. ​  ​
B) ​ 
C) ​ 
D) ​ 
E) ​

Quizplus · Accepted Answer

For a function to be a probability density function, it must satisfy the following two conditions:
1. The function must be non-negative.
2. The integral of the function over the entire domain must be equal to 1.

The given function is:
f(x) = kx^2 for 0 ≤ x ≤ 1

To satisfy the first condition, k must be non-negative, i.e., k ≥ 0.

To satisfy the second condition, we need to integrate the function over the entire domain:
∫(0 to 1) kx^2 dx = 1

Solving this integral, we get:
k/3 = 1
k = 3

Therefore, the value of k such that the function is a probability density function in the given interval is k = 3. Choice C is the correct answer.

Find the Value of the Constant K So That the Function