There are 20 different pairs of shoes. Pick at random 10 shoes. Let X be the number of paired shoes, M be the number of shoes that are left-foot, N be the number of shoes that are right-foot. (a) Find the distribution
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!
There are 20 different pairs of shoes. Pick at random 10 shoes. Let X be the number of paired shoes, M be the number of shoes that are left-foot, N be the number of shoes that are right-foot.
(a) Find the distribution of X. Show your problem-solving process (not just the final answer) with a few sentences of explanation and give the formula
(b) Let Y = M – N. Give all possible values of Y. Find the distribution of Y. Show your problem-solving process (not just the final answer) with a few sentences of explanation and give the formula.
(c) let Z = |Y|, compute E(X), Var(X), E(Z) and Var(Z). Show your problem-solving process (not just the answer), keep 2 decimal places for E(X) and E(Z), and use the approximate values for the calculations of Var(X) and Var(Z).
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