Volume Of Cube Cuboid And Cylinder

Step 1: Assign probabilities
Let , so .
As the total probability is 1: Thus, , and .
Step 2: Define the random variable
Let represent the number of sixes. The possible values of are .
Step 3: Compute probabilities for

Step 4: Probability distribution of

Step 5: Compute the mean of
The mean is given by:
Step 6: Final result
The probability distribution of is: The mean of the distribution is .

Step 1: Reflexivity
For : Thus, , and is reflexive.
Step 2: Symmetry
Let , so: Now, check if : For example: Thus, is not symmetric.
Step 3: Transitivity
Let and , so: Check if : For example: This is irrational, but a counterexample exists for other values. Thus, is not transitive.
Step 4: Final conclusion
The relation is reflexive but neither symmetric nor transitive.