Question

determine whether the distribution is a probability distribution.
x 0 1 2 3 4 5
p(x) 1/5 1/25 3/4 1/10 1/50 1/2
is the probability distribution a discrete distribution? why? choose the correct answer below.
a. yes, because the distribution is symmetric.
b. no, because some of the probabilities have values greater than 1 or less than 0.
c. yes, because the probabilities sum to 1 and are all between 0 and 1, inclusive.
d. no, because the total probability is not equal to 1.

Explanation:

Step1: Check individual probabilities

Check if each \( P(x) \) is between 0 and 1.

• \( \frac{1}{5} = 0.2 \) (0 - 1), \( \frac{1}{25} = 0.04 \) (0 - 1), \( \frac{3}{4} = 0.75 \) (0 - 1), \( \frac{1}{10} = 0.1 \) (0 - 1), \( \frac{1}{50} = 0.02 \) (0 - 1), \( \frac{1}{2} = 0.5 \) (0 - 1). All are in [0,1].

Step2: Sum the probabilities

Calculate \( \frac{1}{5} + \frac{1}{25} + \frac{3}{4} + \frac{1}{10} + \frac{1}{50} + \frac{1}{2} \).
Convert to 50 denominator:
\( \frac{10}{50} + \frac{2}{50} + \frac{37.5}{50} + \frac{5}{50} + \frac{1}{50} + \frac{25}{50} = \frac{10 + 2 + 37.5 + 5 + 1 + 25}{50} = \frac{80.5}{50} = 1.61 \).
Sum is not 1. So total probability ≠ 1.

Answer:

D. No, because the total probability is not equal to 1.