Consider the following situation:

A baseball batter has a .250 batting average (i.e. is successful at hitting the ball 25% of the time). Design a simulation that you would conduct to determine the experimental probability of the batter hitting the ball at least 1 out of 4 times successfully. Remember to:

identify which object you would use to simulate this event

describe what result(s) would represent a favourable outcome and which results would represent an unfavourable outcome

explain what constitutes a single trial for this experiment

How would you expect the experimental probability to compare with the theoretical probability after performing many trials?

'14 (a) if. X is a "modem variable such that 61X] = 3 and 6111\"] = 13, use the Chebyshev inequality to determine a lower bound for P[-2 2). (d) The Chebyshev inequality gives a bound that is less than four times P(|X | 2 1) and gives a bound that is less than four times P(|X | > 2).Consider a discrete random variable X with Rng(X) = {0, 100 } and px = (p, (1-p)) (we can think of this as 100 * a Bernoulli R.V.). This is intended to be a tentative "worst case" for an outlier for which the Markov and Chebyshev inequalities provide some limits. (a) Determine the probability P( X 2 100) using the Markov Inequality. (b) Determine the same probability using the Chebyshev Inequality