(a) Using this graph you can computed the probability of getting the sum of two dice to equal 4 by computing the area of the rectangle above the number four on the graph. In this example the base of the rectangle 3 equals 1 and the height is equal to Putting this together gives us 36 3 P (x = 4) = base height = 1 · 36 Use the area of the shaded region to find the probability of getting a dice roll sum with an odd number. (b) Mark the expected value u = 7 on the probability density curve in figure 1. Measure out one standard deviation above u = 7 on horizontal axis and one standard deviation below µ. Use the standard deviation o = 2.42. Page 2
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) P(Z=4) =?
The sum is equal to 4, and the probability from the graph is
that is, for 4 on x-axis the value on y-axis is
The area of the rectangle = base x height = 1 x =
Now, the probability that the sum is an odd number is given by:
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