need help with this problem: Construct a probability distribution for this game by
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!
I need help with this problem:
-
Construct a
probability distribution for this game by completing the table. -
Compute the
expected value (themean ) of ?. -
Explain the meaning of the expected value ? in the context of the problem.
When a die is rolled the possible outcomes are {1,2,3,4,5,6} with equal probability 1/6.
If the number of die rolled is more than 5 then the amount gained is $8.
If the number on die rolled is less than or equal to 5 then the amount loss is $2.
Let X denote the profit of the game of amount won or loss
1)
The probability distribution table is constructed below.
| Outcome | X | probability |
| 1 | -2 | 1/6 |
| 2 | -2 | 1/6 |
| 3 | -2 | 1/6 |
| 4 | -2 | 1/6 |
| 5 | -2 | 1/6 |
| 6 | +8 | 1/6 |
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