Question

Let x be a discrete random variable with pmf f(x) = log

Answer 1

The sum of the probabilities is 1.

Step-by-step explanation:

A discrete random variable is one that can only take on a finite or countable number of values. In this case, the random variable X takes on the values 0, 1, 2, 3, 4, 5, so it is discrete. Additionally, a probability mass function (pmf) is used to describe the probabilities of each value of a discrete random variable. The pmf of X is given as f(x) = log, which means that the probability of each value is equal to the logarithm of that value. For example,
`f(1) = log(1) = 0`.

To find the sum of the probabilities, we can calculate
`f(0) + f(1) + f(2) + f(3) + f(4) + f(5)`. Since log(1) = 0, we can simplify the sum as
`log(2) + log(3) + log(4) + log(5) = log(120)`. Therefore, the sum of the probabilities is 1.