Verify that the following function is a probability mass function, and determine the requested probabilities. f left-parenthesis x right-parenthesis equals left-parenthesis 27divided by 13right-parenthesis left-parenthesis 1 divided by 3right-parenthesis Superscript x ,

1)

2)

We can find the individual probabilities and we got:

And the sum of the 3 values 0.6923+0.2307+0.0770= 1 so then we satisfy all the conditions and we can conclude that f(x) is a probability distribution.

Step-by-step explanation:

For this case we have the following density function:

In order to satisfty that this function is a probability mass function we need to check two conditions:

1)

2)

We can find the individual probabilities and we got:

And the sum of the 3 values 0.6923+0.2307+0.0770= 1 so then we satisfy all the conditions and we can conclude that f(x) is a probability distribution.

And if we want to find the following probabilities:

6-3=3

3*3=9

9+12=21

21/3=7

7*8=56

56 is your answer