Question

Determine whether the given values can be looked upon as the values of a probability distribution of a random variable that can take on the values 1, 2, 3,4 , and 5 . Answer yes or no. If no, explain why not.

A.f(1)=0.18
B.f(2)=0.20
C.f(3)=0.22
D.f(4)=0.23
E.f(5)=0.18

Answer 1

The given values cannot be considered a probability distribution for the discrete random variable, since the sum of the probabilities (1.01) exceeds the required total of 1.0.

Step-by-step explanation:

Verification of Probability Distribution

For a set of values to be considered as a probability distribution for a discrete random variable, two conditions must be met:

• The probability of each event must be between 0 and 1, inclusive.
• The probabilities must sum to exactly 1.0, representing the certainty that some outcome must occur.

In the given scenario, the random variable can take on the values 1, 2, 3, 4, and 5 with respective probabilities:

• f(1) = 0.18
• f(2) = 0.20
• f(3) = 0.22
• f(4) = 0.23
• f(5) = 0.18

To verify if this is a valid probability distribution:

1. Check individual probabilities: Each given probability is between 0 and 1, which is valid.
2. Sum the probabilities: 0.18 + 0.20 + 0.22 + 0.23 + 0.18 = 1.01, which exceeds 1.0.

Since the sum of the probabilities is greater than 1.0, this set of values cannot be considered a valid probability distribution.