An unfair die looks like an ordinary six-sided die but the outcomes are not equally likely. The probability distribution of the face value, $\displaystyle {X}$, is as follows:

$\displaystyle {x}_{{i}}$	0	1	2	3	4	5	6	Total
$\displaystyle {P}{\left({X}={x}_{{i}}\right)}$	0.02	0.11	0.2	0.33	0.19	0.13	0.02	1

1. Use the random variable notation to express symbolically each of the following:
   • -X=5 P(X=3) P(X=4)=0.19  The probability that the face value is exactly 4 is equal to 0.19.
   • -X=5 P(X=3) P(X=4)=0.19  An event in which the face value is exactly 5.
   • -X=5 P(X=3) P(X=4)=0.19  The probability that the face value is exactly 3.

    
2. Use the above probability distribution table to find the following:
   1. $\displaystyle {P}{\left({3}<{X}\le{4}\right)}=$ (Round the answer to 2 decimals)
   2. $\displaystyle {P}{\left({1}<{X}\le{3}\right)}=$ (Round the answer to 2 decimals)
   3. $\displaystyle {P}{\left({X}\le{5}\right)}=$ (Round the answer to 2 decimals)