Final answer:
A binomial random variable represents the number of successes in a fixed number of independent trials. The mean and standard deviation can be calculated using the formulas µ = np and σ = √(npq). The probability of obtaining a certain number of successes can be calculated using the binomial probability formula.
Step-by-step explanation:
The question is asking about two binomial random variables with parameters (n, p1) and (n, p2). A binomial random variable is a discrete random variable that arises from Bernoulli trials. It represents the number of successes in a fixed number of independent trials. The parameters n represents the number of trials and p represents the probability of success on each trial.
The mean of a binomial random variable can be calculated using the formula µ = np, where µ is the mean and n is the number of trials. The standard deviation is given by the formula σ = √(npq), where σ is the standard deviation and q is the probability of failure on each trial (q = 1 - p).
To find the probability distribution for each binomial random variable, you can use the formula P(X = x) = (nCx) * (p^x) * (q^(n-x)), where P(X = x) is the probability of x successes, nCx is the number of combinations of n items taken x at a time, p^x is the probability of x successes, and q^(n-x) is the probability of n-x failures.