A coin is tossed 4 times. Find the mean and variance of the probability distribution of the number of tails.

Answer

To find the mean and variance of the probability distribution of the number of tails when a coin is tossed 4 times, we can follow these steps:

### Step 1: Identify the parameters
In this problem, we have:
- Number of trials (n) = 4 (since the coin is tossed 4 times)
- Probability of getting tails (P) = 1/2
- Probability of getting heads (Q) = 1 - P = 1/2

### 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:
\[ \mu = 4 \cdot \frac{1}{2} = 2 \]

### 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:
\[ \sigma^2 = 4 \cdot \frac{1}{2} \cdot \frac{1}{2} = 4 \cdot \frac{1}{4} = 1 \]

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