Question

A discrete random variable X has the following probability distribution:

X:	0	1	2	3	4	5
P(X):	b	3b	5b	3b	4b	6b

The value of b is:

• A. \(\frac{1}{25}\)
• B. \(\frac{1}{5}\)
• C. \(\frac{1}{22}\)
• D. 1

Answer 1

The Correct Option is C

To find the value of \( b \), we must use the fact that the sum of all probabilities of a discrete random variable equals 1. Given the probability distribution:

X:	0	1	2	3	4	5
P(X):	b	3b	5b	3b	4b	6b

We calculate the total probability sum:

\[ b + 3b + 5b + 3b + 4b + 6b = 1 \]

Simplifying this, we get:

\[ 22b = 1 \]

Solving for \( b \), we divide both sides by 22:

\[ b = \frac{1}{22} \]

Therefore, the value of \( b \) is \(\frac{1}{22}\).