1. what is the sum of the probabilities in a discrete probability distribution? why?

Sum of probabilities in a discrete probability distribution is 1.

Step-by-step explanation:

The sum of the probabilities in a probability distribution is always 1.

A probability distribution is a collection of probabilities that defines the likelihood of observing all of the various outcomes of an event or experiment. Based on this definition, a probability distribution has two important properties that are always true:

Each probability in the distribution must be of a value between 0 and 1.

The sum of all the probabilities in the distribution must be equal to 1.

first option

a function is a relation in which an input is paired with exactly one output.

so, let's find the right answer.

in our first option, our inputs are january, february, and march. the outputs are 30, 28, and 25. each input has it's own output. this is correct!

our second option we know is incorrect, because ms. valverade has two outputs, dogs and cats. this is not a function.

our third option is incorrect as well. the yellow square has two ouputs, the square and the triangle.

lastly, in our fourth option, we see the number 7 two times with a different output. therefore, this is not a function.

remember: each input must be paired with only one output!

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step-by-step explanation: