A professor spends a time every day to go from home to work, represented by the Y random variable given by the distribution below. g1601 1 у, 25 0 sy< 5 2 1 g1601 y, 5 10 A E [Y] = = 0.92 g160 00555 - 9871 = 15, P (Y <8) = C E[ ( .92 1944 g160100555-987047944 g160100555 -987047944/ = 0 916 E [Y] = ,P (Y <8) = 0.8 g160100555 -987047944/ 441 g160100555 - 987047944 0441 g16r 0441
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 professor spends a time every day to go from home to work, represented
by the Y random variable given by the distribution below.
g1601
1
у,
25
0 sy< 5
2
1
y, 5<y<10
25
g1601
5
0,
y > 10
Given that E [Y] = ?, P (Y <8) =?
g16010055598704
E [Y] =
A
= 0.92
g160100555 -9870479441
P (Y <8) =
g160100555 -987047944
=
= 0
9160
E [Y]
= 1/5, P
(Y <8) = 0.8
g160100555-987047944
441
g160100555 - 987047944
0441
g16r
0441](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe757ffb7-2112-492c-825b-c56f3498d561%2Fd1e2627d-3cb1-43a7-88d4-15184d6c830e%2Fpe2c6wn_processed.jpeg&w=3840&q=75)
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