Expected Value: Show me the Money. A wallet contains 6 five-dollar bills and 4 one- ollar bills. Two bills are randomly selected (without replacement) and their total is oted. List the possible values for the random variable X = TOTAL value of the two bills Du might select. Then determine the probability that each of these totals might occur: a. p(x) $2 ($1 followed by $1)
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!
![**7. Expected Value: Show me the Money**
A wallet contains 6 five-dollar bills and 4 one-dollar bills. Two bills are randomly selected (*without replacement*) and their total is noted. List the possible values for the random variable \( X = \text{TOTAL value of the two bills you might select}\). Then determine the probability that each of these totals might occur:
a.
\[
\begin{array}{c|c}
x & p(x) \\
\hline
\$2 \, \text{($1 \text{ followed by } \$1$)} & \left( \, \, \right) * \left( \, \, \right) = \\
& \left( \, \, \right) * \left( \, \, \right) + \left( \, \, \right) * \left( \, \, \right) = \\
\end{array}
\]
b. Find the expected value (mean) for the total value of the two bills selected: $ _______
c. Find the standard deviation: $ _______
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(Note: The table has empty parentheses for students to calculate probabilities based on combinations of the bills selected.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1064d08b-e094-4e7d-bb6f-10908ee8847f%2F0c53fbab-91b6-4701-802a-10e5cdd8f0bd%2Foo8jrr_processed.jpeg&w=3840&q=75)
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