To find the probability P(X = 10) for a discrete uniform random variable ranging from 0 to 12, we first need to understand the properties of a discrete uniform distribution.
A discrete uniform random variable is one where each value in the specified range has an equal probability of occurring. In this case, the random variable X can take on any integer value from 0 to 12, inclusive.
Let’s determine the total number of possible values for X. Since X can take values from 0 to 12, we have:
- Values: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
Counting these, we find there are:
- Total values = 12 – 0 + 1 = 13
Now that we know there are 13 equally likely outcomes, the probability of any specific value (including X = 10) is given by:
P(X = k) = 1 / Number of possible values
Substituting the values we have, we find:
P(X = 10) = 1 / 13
Thus, the probability of the discrete uniform random variable X being equal to 10 is:
P(X = 10) ≈ 0.0769
In conclusion, P(X = 10) is approximately 0.0769, indicating that there is about a 7.69% chance of X being equal to 10.