Question

determine whether the distribution is a probability distribution.

x	0	1	2	3	4	5
p(x)	3/5	1/10	1/50	1/25	1/20	1/4

is the probability distribution a discrete distribution? why? choose the correct answer below.
a. yes, because the probabilities sum to 1 and are all between 0 and 1, inclusive.
b. no, because the total probability is not equal to 1.
c. no, because some of the probabilities have values greater than 1 or less than 0.
d. yes, because the distribution is symmetric.

Explanation:

Step1: Calculate sum of probabilities

$P=\frac{3}{5}+\frac{1}{10}+\frac{1}{50}+\frac{1}{25}+\frac{1}{20}+\frac{1}{4}$
First, find a common - denominator. The least common multiple of 5, 10, 50, 25, 20 and 4 is 100.
$P=\frac{3\times20}{5\times20}+\frac{1\times10}{10\times10}+\frac{1\times2}{50\times2}+\frac{1\times4}{25\times4}+\frac{1\times5}{20\times5}+\frac{1\times25}{4\times25}$
$P = \frac{60}{100}+\frac{10}{100}+\frac{2}{100}+\frac{4}{100}+\frac{5}{100}+\frac{25}{100}$
$P=\frac{60 + 10+2 + 4+5+25}{100}=\frac{106}{100}=1.06$

Step2: Check conditions for discrete probability distribution

For a discrete probability distribution, the sum of all probabilities must be equal to 1 and each probability value must be between 0 and 1 (inclusive). Since the sum of the given probabilities is 1.06 which is not equal to 1, it is not a discrete probability distribution.

Answer:

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