a)
A random variable is a function that associates a real number with each element in the sample space.
The distinction between a discrete and a continuous random variable is the same as the distinction between a discrete and a continuous frequency distribution: only certain results are possible for a discrete random variable, but any of an infinite number of results within a certain range are possible for a continuous random variable.
If a sample space contains a finite number of possibilities or an unending sequence with as many elements as there are whole numbers, it is called a discrete sample space.
If a sample space contains an infinite number of possibilities equal to the number of points on a line segment, it is called a continuous sample space.
The amount of coffee dispensed by the machineis a continuous random variable, because its value can be any real number between 10 and 13 ounces, inclusive.
b) The probability density function of the continuous uniform random variable X on the interval [10, 13] is
c)
d)
Find the probability that my 12 oz. cup will not overflow
How large of a coffee cup should I have if I want to be 95% confident that the dispenser would not overfill the cup?
"k=3(0.95)+10=12.85"
I take 12.85 oz. coffee cup.
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