(a) Find the probability that he strikes out for the first time in his 5th plate appearance. (b) Find the probability that he reaches base safely for the 4th time in his 8th plate appearance. (c) Given that he has reached base safely 3 times in his first 5 plate appearances, find the probability that the 7th plate appearance is the 4th time he reaches base safely.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
For each plate appearance, a baseball player either reaches base safely with
(a) Find the probability that he strikes out for the first time in his 5th plate appearance.
(b) Find the probability that he reaches base safely for the 4th time in his 8th plate appearance.
(c) Given that he has reached base safely 3 times in his first 5 plate appearances, find the
probability that the 7th plate appearance is the 4th time he reaches base safely.
(d) Find the expected number of strikeouts in his first 10 plate appearances.
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