Questions: State whether the function is a probability mass function or not. If not, explain why not.
f(x)=1/14 x, for x=2,3,4,5
Select all that apply.
A. The function f(x) is a probability mass function.
B. The function f(x) is not a probability mass function because it does not satisfy the third condition of probability mass functions.
C. The function f(x) is not a probability mass function because it does not satisfy the first condition of probability mass functions.
D. The function f(x) is not a probability mass function because it does not satisfy the second condition of probability mass functions.
Transcript text: State whether the function is a probability mass function or not. If not, explain why not.
\[
f(x)=\frac{1}{14} x, \text { for } x=2,3,4,5
\]
Select all that apply.
A. The function $f(x)$ is a probability mass function.
B. The function $f(x)$ is not a probability mass function because it does not satisfy the third condition of probability mass functions.
C. The function $f(x)$ is not a probability mass function because it does not satisfy the first condition of probability mass functions.
D. The funmtion $f(x)$ is not a probability mass function because it does not satisfy the second condition of probability mass functions.
Solution
Solution Steps
Step 1: Check for Non-negativity
All probabilities are non-negative, satisfying the first condition of a PMF.
Step 2: Check for Normalization
The sum of all probabilities equals 1, satisfying the second condition of a PMF.
Step 3: Check for Discreteness
All outcomes are discrete, satisfying the discreteness condition of a PMF.
Final Answer:
The given function represents a valid Probability Mass Function (PMF).