Suppose that a person’s score X on a mathematics aptitude test is a number between 0 and 1 and that his score Y on a music aptitude test is also a number between 0 and 1. Suppose further that in the population of all college students in Belize, the scores X and Y redistributed according to the following joint pdf. f(x,y) = 2/5(2x + 3y) for 0≤x≤1, 0≤y≤1 and 0 otherwise What proportion of college students obtain a score greater than 0.8 on the mathematics test? If a student’s score on the music test is 0.3, what is the probability that his score on the mathematics test will be greater than 0.8?
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!
Suppose that a person’s score X on a mathematics aptitude test is a number between 0 and 1 and that his score Y on a music aptitude test is also a number between 0 and 1. Suppose further that in the population of all college students in Belize, the scores X and Y redistributed according to the following joint
f(x,y) = 2/5(2x + 3y) for 0≤x≤1, 0≤y≤1 and 0 otherwise
- What proportion of college students obtain a score greater than 0.8 on the mathematics test?
- If a student’s score on the music test is 0.3, what is the
probability that his score on the mathematics test will be greater than 0.8?
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