Question

For the probability distribution function of random variable X ,$x_1,x_2,x_3,....x_n$ are the values X takes, and $p\left(x_i\right)$ denote the probability of $x_i$ then which one of the following is true.?

• A. $p\left(x_i\right)>0$
• B. $p\left(x_i\right)<0$
• C. $\sum p\left(x_i\right)=1$
• D. $\sum x_i=1$

Answer 1

Answer: (A), (C)

The correct options are
A $p\left(x_i\right)>0$
C $\sum p\left(x_i\right)=1$

The probability distribution function of a random variable is a list of probabilities associated with each of its possible values.

Suppose a random variable $X$ may take $k$ different values, with the probability that $X=x_i$ defined to be $P(X=x_i)=p_i$. The probabilities $p_i$ must satify the following:

$0\le p_i\le 1$ for each $i$.

$p_1+p_2+...+p_k=1$ that is $\sum p_i=1$

Thus $\left(A\right)$ and $\left(C\right)$ are true.