Test the following function to determine whether it is a probability function. If it is not, then make it into a probability function. (Give your answers correct to one decimal place.)
R(x) = 0.2, for x = 0, 1, 2, 3, 4
(a) List the distribution of probabilities.
R(0) =
R(1) =
R(2) =
R(3) =
R(4) =
To determine whether the given function R(x) is a probability function, we need to check if the probabilities sum to 1 for all possible values of x.
(a) Let's list the distribution of probabilities for the function R(x):
R(0) = 0.2
R(1) = 0.2
R(2) = 0.2
R(3) = 0.2
R(4) = 0.2
Now, let's check if these probabilities sum up to 1:
R(0) + R(1) + R(2) + R(3) + R(4) = 0.2 + 0.2 + 0.2 + 0.2 + 0.2 = 1.0
Since the sum of probabilities is equal to 1, the given function R(x) is already a probability function.
In order to determine whether the given function R(x) is a probability function, we need to check if the sum of all probabilities is equal to 1. Let's calculate the sum of probabilities:
R(0) = 0.2
R(1) = 0.2
R(2) = 0.2
R(3) = 0.2
R(4) = 0.2
Now, let's calculate the sum of these probabilities:
Sum = R(0) + R(1) + R(2) + R(3) + R(4)
Sum = 0.2 + 0.2 + 0.2 + 0.2 + 0.2
Sum = 1.0
The sum of probabilities is equal to 1, which means that the given function R(x) is already a probability function. Therefore, there is no need to make any changes to it.
The distribution of probabilities is as follows:
R(0) = 0.2
R(1) = 0.2
R(2) = 0.2
R(3) = 0.2
R(4) = 0.2