Question

The mean of Binomial distribution \(B(4,\frac13) \) is : 

• A. \(\frac43\)
• B. \(\frac23\)
• C. \(\frac83\)
• D. \(\frac13\)

Answer 1

The Correct Option is A

The mean of a binomial distribution is calculated using the formula \(\mu = n \cdot p\), where \(n\) is the number of trials and \(p\) is the probability of success in each trial. For the binomial distribution \(B(4,\frac{1}{3})\), we have:

• \(n = 4\)
• \(p = \frac{1}{3}\)

Substitute these values into the formula to find the mean:

\[\mu = 4 \cdot \frac{1}{3} = \frac{4}{3} \]

Thus, the mean of the binomial distribution \(B(4,\frac{1}{3})\) is \(\frac{4}{3}\).

Option	Value
\(\frac{4}{3}\)	Correct
\(\frac{2}{3}\)	Incorrect
\(\frac{8}{3}\)	Incorrect
\(\frac{1}{3}\)	Incorrect