Question

question 1 consider the following table. here x is a random variable with corresponding probability p(x). is this a probability distribution? why or why not? x p(x) 4 0.4 5 0.2 6 0.34 7 0.2 no. because i said so! yes, it is a probability distribution. no. the sum off all probabilities exceeds 1. no. we dont know what 4,5,6 and 7 represent. 3 pts

Explanation:

Step1: Recall probability - distribution rule

For a probability - distribution, the sum of all probabilities $P(X)$ must equal 1, i.e., $\sum_{i}P(X_i)=1$, where $X_i$ are all possible values of the random variable $X$.

Step2: Calculate the sum of given probabilities

$P(4)+P(5)+P(6)+P(7)=0.4 + 0.2+0.34 + 0.2=1.14$.

Answer:

No. The sum of all probabilities exceeds 1.