Question 1184134
Here's how to analyze the experiment of throwing two coins:

**a. Probability Distribution:**

First, let's list the sample space (all possible outcomes):

* HH (Heads, Heads)
* HT (Heads, Tails)
* TH (Tails, Heads)
* TT (Tails, Tails)

Since the coins are fair, each outcome has an equal probability of 1/4.

Let X be the random variable representing the number of heads.  The possible values of X are 0, 1, and 2.  We can now create the probability distribution:

* P(X = 0) = P(TT) = 1/4
* P(X = 1) = P(HT) + P(TH) = 1/4 + 1/4 = 2/4 = 1/2
* P(X = 2) = P(HH) = 1/4

Here's the probability distribution in table form:

| X (Number of Heads) | P(X) |
|---|---|
| 0 | 1/4 |
| 1 | 1/2 |
| 2 | 1/4 |

**b. Expected Value (E[X] or μ):**

The expected value is calculated as:

E[X] = Σ [x * P(X = x)]

E[X] = (0 * 1/4) + (1 * 1/2) + (2 * 1/4)
E[X] = 0 + 1/2 + 1/2
E[X] = 1

The expected number of heads is 1.

**c. Standard Deviation (σ):**

1. **Calculate the variance (Var[X] or σ²):**

Var[X] = Σ [(x - E[X])² * P(X = x)]

Var[X] = (0 - 1)² * 1/4 + (1 - 1)² * 1/2 + (2 - 1)² * 1/4
Var[X] = 1 * 1/4 + 0 * 1/2 + 1 * 1/4
Var[X] = 1/4 + 0 + 1/4
Var[X] = 1/2 = 0.5

2. **Calculate the standard deviation (σ):**

σ = √Var[X]
σ = √(1/2)
σ ≈ 0.707

The standard deviation of the number of heads is approximately 0.707.