Question

First, decide whether the distribution is a discrete probability distribution, then select the reason for making this decision.
$x: -2, 2, 10$

$P(X=x) : 0.39, 0.69, 0.12$

Decide: Yes or no?

Reasons:
a) Since the probabilities lie inclusively between 0 and 1 and the sum of the probabilities is equal to 1

b) Since at least one of the probability values is greater than 1 or less than 0

c) Since the sum of the probabilities is not equal to 1

d) Since the sum of the probabilities is equal to 1

e) Since the probabilities is lies inclusively between 0 and 1

Answer 1

It is not a probability distribution, as the sum of the probabilities is more than 1, thus, the correct option is No, considering that:

c) Since the sum of the probabilities is not equal to 1.

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For the sequence $(x, P(X = x))$ representing a probability distribution, it is needed that:

• All probabilities are between 0 and 1, that is, for all values of x, $0 \leq P(X = x) \leq 1$.
• The sum of all probabilities is 1, that is: $\sum_{i = 1}^n P(x_i) = 1$

In this problem, the sum of the probabilities is:

$\sum_{i = 1}^n P(x_i) = 0.39 + 0.69 + 0.12 = 1.20$

Sum is not 1, thus it is not a probability distribution, and the correct option is:

c) Since the sum of the probabilities is not equal to 1.

A similar problem is given at https://brainly.com/question/24858659