Assuming a binomial experiment with p = 0.5 and a sample size of 100. The expected value of this distribution is?

Step 1: Break Down the Problem

To find the expected value of a binomial distribution, we need to understand the parameters involved:

• $p$: the probability of success in a single trial, which is given as $p = 0.5$.
• $n$: the number of trials (sample size), which is given as $n = 100$.

Step 2: Relevant Concepts

The formula for the expected value $E(X)$ of a binomial distribution is given by: $E(X) = n \cdot p$

Step 3: Analysis and Detail

Substituting the values of $n$ and $p$ into the formula: $E(X) = 100 \cdot 0.5$

Step 4: Verify and Summarize

Calculating the expected value: $E(X) = 100 \cdot 0.5 = 50$ The calculation is straightforward and checks out.

Final Answer

The expected value of this binomial distribution is $50$.