Question

If X follows binomial distribution with parameters n = 10, p = 0.2. Then mean of the random variable X is

• A. 10
• B. 0.2
• C. 2
• D. 1.6

Hint:

Remember the core properties of a Binomial distribution: Mean = $np$ and Variance = $np(1-p)$.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
A binomial distribution is characterized by the number of independent trials $n$ and the probability of success in each trial $p$.
Key Formula or Approach:
The mean (expected value) of a binomial random variable $X$ is given by the formula:
\[ E(X) = n \times p \]

Step 2: Detailed Explanation:
We are given:
Number of trials, $n = 10$
Probability of success, $p = 0.2$
Substitute these parameter values into the mean formula:
\[ E(X) = 10 \times 0.2 = 2 \]
Therefore, the mean of the random variable $X$ is 2.

Step 3: Final Answer
The correct option is (C).