Question

the probability function of a discrete random variable x is given by p(x) = q x x = 1 2 3 4

1. value of q
2. probability distribution table of x
3. mean

Answer 1

$$p(x)=qx, x=1,2,3,4$$

1. value of $q$

$$q(1)+q(2)+q(3)+q(4)=1$$ $$q=0.1$$

2. probability distribution table of x 

$$\def\arraystretch{1.5} \begin{array}{c:c} x & 1 & 2 & 3 & 4 \\ \hline p(x) & 0.1 & 0.2 & 0.3 & 0.4 \\ \end{array}$$

3. mean

$$mean=\mu_X=E(X)=$$ $$=1(0.1)+2(0.2)+3(0.3)+4(0.4)=3$$