Question

Determine whether or not the following distribution is a probability distribution. If the distribution is not a probability distribution, give the characteristic which is not satisfied by the distribution.

P(X=x)=x+4 /15, for x=−5,−4,−3,−2,−1

Answer 1

The given distribution is not a probability distribution because the sum of probabilities does not equal 1.

Step-by-step explanation:

To determine whether or not the given distribution is a probability distribution, we need to check if the probability of all possible outcomes adds up to 1 and if all probabilities are non-negative.

Let's calculate the probabilities:

• P(X=-5) = (-5+4)/15 = -1/15
• P(X=-4) = (-4+4)/15 = 0/15 = 0
• P(X=-3) = (-3+4)/15 = 1/15
• P(X=-2) = (-2+4)/15 = 2/15
• P(X=-1) = (-1+4)/15 = 3/15 = 1/5

Now, let's check the conditions:

• The sum of probabilities is: (-1/15) + 0 + (1/15) + (2/15) + (1/5) = 1/5 + 3/15 = 1/5 + 1/5 = 2/5 + 2/5 = 4/5
• The probabilities are non-negative, except for P(X=-5)

Since the sum of probabilities is not equal to 1, the given distribution is not a probability distribution. The characteristic not satisfied by the distribution is that the sum of probabilities must equal 1.