3.5 3 2.5 2 z а. 1.5 0.5 1.5-1 0.5 0 05 1 1.5 b. 15-1 0.5 0 05 0.5 0 os 1 15 d.
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) Consider the graph a)
It is a graph of family of downward parabolas.
A contour line for a function of two variables is a curve connecting points where the function has the same particular value.
The family of parabolas has the general equation
.
Draw the contour line of this equation as a curve along which the function has constant value.
By joining all the contour lines we get the plane section of the graph as contour the corresponding contour of a is d)
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