You decide to flip a fair coin 100 times.
What is the variance of this distribution?
Also
You decide to flip a fair coin 100 times.
What is the standard deviation of this distribution?
To find the variance and standard deviation of flipping a fair coin 100 times, we first need to understand the concept of probability.
The probability of an event happening is calculated by dividing the number of ways an event can occur by the total number of possible outcomes. In this case, flipping a fair coin has 2 possible outcomes: heads (H) or tails (T), and each outcome has an equal chance of occurring.
Let's start by finding the variance, which measures the spread or dispersion of a distribution. The formula for variance, denoted by σ^2, is given by:
Variance (σ^2) = ∑ (xi - μ)^2 / N
where:
- ∑ (sigma) indicates the sum of the following expression for all i.
- xi represents each individual value in the distribution (either 0 or 1 for the coin flip).
- μ (mu) is the mean or average value of the distribution.
- N is the total number of values in the distribution.
Since we are flipping a fair coin, the mean μ is calculated as the sum of outcomes divided by the total number of trials, which is 0.5 (or 1/2) because each outcome has an equal probability.
μ = (0 + 1) / 2 = 0.5
Now, we can plug in the values into the variance formula:
Variance (σ^2) = [(0-0.5)^2 + (1-0.5)^2] / 100 = 0.25 / 100 = 0.0025
Therefore, the variance of flipping a fair coin 100 times is 0.0025.
To calculate the standard deviation, we take the square root of the variance:
Standard Deviation (σ) = √0.0025 = 0.05
Thus, the standard deviation of flipping a fair coin 100 times is 0.05.