Think about a density curve that consists oftwo straight-line segments. The first goes fromthe point (0, 1) to the point (0.7, 1) then thesecond goes from the point (0.7, 1) to the point(1.3, 0).a. Sketch this density curve:b. What is the probability that X falls below0.5?c. What is the probability that X liesbetween 0.7 and 1.3?d. What is the probability that X lies above0.2?e. What is the probability that X is equal to0.5?
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!
Think about a density curve that consists of
two straight-line segments. The first goes from
the point (0, 1) to the point (0.7, 1) then the
second goes from the point (0.7, 1) to the point
(1.3, 0).
a. Sketch this density curve:
b. What is the
0.5?
c. What is the probability that X lies
between 0.7 and 1.3?
d. What is the probability that X lies above
0.2?
e. What is the probability that X is equal to
0.5?
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