Question

MAC 15

First, consider an 'experiment' where we will toss a fair die and let **X = the number of dots facing up**. of course the possible values for X are 1, 2, 3, 4, 5 and 6 and each of these is equally likely. Show the probability distribution for X using the first two columns in the table below. **Avoid rounding errors, show the probabilities as fractions - not as decimals**. Next fill in the next two columns using fractions. Don't reduce fractions as you'll want to have a common denominator in each column.

* means multiply

x | P(X = x) | x * P(X = x) | x^2 * P(X = x) |

1 | |||

2 | |||

3 | |||

4 | |||

5 | |||

6 | |||

SUM |

a) Express the Expected Value of X, also known as the mean, u, as both a reduced fraction and as a decimal

b) show your work to find variance and standard deviation in both fraction and decimal.

Step 1

Consider the random variable *X*, that is defined as the number of dots facing up in a fair die. The values of *X* are 1,2,3,4,5 and 6, which are equally likely.

The probability of getting *X* is equal to 1:

Step 2

The completed table is shown below:

Step 3

a)

The expected value of *X* can b...

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