An unbiased coin is tossed 4 times. Find the mean and variance of the number of heads obtained.

Answer

To solve the problem of finding the mean and variance of the number of heads obtained when an unbiased coin is tossed 4 times, we can follow these steps:

### Step 1: Identify the parameters
We know that:
- The number of trials (n) = 4 (since the coin is tossed 4 times)
- The probability of success (p) = 1/2 (the probability of getting heads)
- The probability of failure (q) = 1 - p = 1/2 (the probability of getting tails)

### Step 2: Calculate the Mean
The mean (μ) of a binomial distribution can be calculated using the formula:
\[ \mu = n \cdot p \]

Substituting the values we have:
\[ \mu = 4 \cdot \frac{1}{2} = 2 \]

### Step 3: Calculate the Variance
The variance (σ²) of a binomial distribution can be calculated using the formula:
\[ \sigma^2 = n \cdot p \cdot q \]

Substituting the values we have:
\[ \sigma^2 = 4 \cdot \frac{1}{2} \cdot \frac{1}{2} = 4 \cdot \frac{1}{4} = 1 \]

### Final Results
- Mean (μ) = 2
- Variance (σ²) = 1