Final answer:
The probability mass function (PMF) of a binomial random variable can be calculated using the formula P(X = k) = C(n, k) * p^k * (1-p)^(n-k). For p = 0.5 and n = 10, the PMF can be calculated by replacing the variables with their values and summing the probabilities for each value of x from 0 to 10.
Step-by-step explanation:
The probability mass function (PMF) of a binomial random variable can be calculated using the formula:
P(X = k) = C(n, k) * p^k * (1-p)^(n-k)
where:
- X is the binomial random variable
- n is the number of trials
- p is the probability of success on each trial
- k is the number of successes
- C(n, k) is the number of ways to choose k successes from n trials, which can be calculated using the combination formula C(n, k) = n! / (k! * (n-k)!)
In this case, with p = 0.5 and n = 10, the PMF of x can be calculated by replacing the variables with their values and summing the probabilities for each value of x from 0 to 10. For example, P(x = 0) = C(10, 0) * 0.5^0 * (1-0.5)^(10-0) = 0.000977