Binomial Distribution

Let Mean = , Variance = Difference: Since , Now, find using binomial formula: % Final Answer

The mean and variance of a binomial distribution are given by: Using the given values and , we solve for and . The solution gives and .

Let be a binomial random variable. The probability mass function of a binomial random variable is given by: We are given that . Hence, we have: Simplifying: Now, we need to calculate , which is equivalent to . Using the binomial distribution: Using the values of and the binomial probabilities: Thus, the correct answer is .