what is the expected value of the distance
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!
A shape of a university campus is a square with side length of 10 miles. If you imagine the university on the x-y plane, in the first quadrant with two sides of the square on the positive axes, then the student union is at the origin (at a corner of the square). At noon on a certain day an announcement was made that all students had to walk to the student union. At that time the density
f(x, y) = (3/20000)*(x^2 + y^2 ) 0 < x < 10, 0 < y < 10,
0 otherwise.
If students are only allowed to walk parallel to the axes what is the expected value of the distance walked to the student union by a randomly chosen student on campus? (Assume that students walk in a way that monotonically decreases their distance to the student union. That is, they don’t walk ” backward”.)
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