Variance And Standard Deviation

We are given that 7 coins are tossed simultaneously, and the random variable represents the number of heads. We are asked to find , where is the mean and is the variance of .
Step 1: Since we are tossing 7 coins, the number of heads follows a binomial distribution with parameters and . The probability mass function for a binomial random variable is given by: Substitute and to find the probabilities.
Step 2: The mean of a binomial distribution is given by: The variance of a binomial distribution is given by: Step 3: Now, calculate , which is the probability of getting exactly 3 heads: First, calculate the binomial coefficient: Thus, Step 4: We are asked to find . Substituting the values of and : Thus, .