Question

~ is a random variable that has two different distributions, () and ().
() is presented in the following table, while () is defined as ()=(2 +1)2
a) Determine () for each value of the random variable X.
X
-3
6
9
()
1/6
1/2
1/3
()
b) Determine whether each of () or () can be a probability distribution. Explain.

Answer 1

Whatever distribution is used the sum of all the probabilities must be 1. It’s not clear what the formula is in this question because of typing anomalies. However, the tabulated data has the right property of a distribution, because ⅙+½+⅓=1 so in answer to part (b) this could well be a probability distribution.

As for the other distribution, there is insufficient information, and x is absent from the formula, so we can’t judge whether it’s a possible probability distribution or not.  Check and resubmit the formula. The sum total of probabilities for all values of x must add up to 1, so, for example, (2x+1)² couldn’t be a probability function, because each probability would be greater than 1, and the sum would be greater than 1.