Question

For a given probability density function, determine the value of "k" that makes it valid. What condition μst be satisfied for a function to be a valid probability density function?

a) k > 1
b) k = 0
c) k > 0 and k <= 1
d) k = 1

Answer 1

The value of 'k' that makes a probability density function valid is such that the total area under the curve equals 1, thus the correct answer is 'd) k = 1'.

Step-by-step explanation:

To determine the value of "k" that makes a probability density function (pdf) valid, we must adhere to one important condition: the area under the pdf (and above the x-axis) must equal 1. This is because in a continuous probability distribution, probability is equivalent to the area under the probability density curve. Consequently, for a function to be a valid probability density function (pdf), the condition that must be satisfied is 'd) k = 1'.