Probability, Random Variables, and Probability Distributions
If the probability of success on a single trial in a binomial experiment is 0.2 and we want to find the probability of exactly three successes in ten trials, which calculation is appropriate?
If the probability that an individual randomly selected from a population prefers brand A over brand B is 0.3, and you select 150 individuals at random, which of the following is the approximate standard deviation of the number of individuals who prefer brand A?
If you were told that only six out of twenty sampled marbles drawn at random are blue and assuming these draws represent Bernoulli trials, what information would you still require to determine if this forms part of data appropriately modeled by the binomial distribution?
When increasing the number of trials in a binomial experiment, what is the effect on the shape of the distribution if p remains constant?
What is the maximum likelihood estimator (MLE) for the parameter p in a binomial distribution where k=800 successes were observed over 4000 trials?
When flipping a fair coin three times, what parameter represents the expected number of tails?
When flipping an unbiased coin three times, how many outcomes have at least one head appearing?
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How does increasing only the probability of success ('p') while keeping the number of trials ('n') constant affect the standard deviation of a binomial distribution?
What is the probability of success in a binomial distribution called?
What would most likely invalidate using binomial distribution when investigating if having attended pre-school affects college acceptance rates among high school seniors?