Answer:
E(X)=3.125
Step-by-step explanation:
We are given that two four sided dice.
Then , the sample space
{(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(2,4),(3,1),(3,2),(3,3),(3,4),(4,1),(4,2),(4,3),(4,4)}
Total number of outcomes=16
Let the random variable X represent the maximum value of the two dice
Outcomes X P(X)
(1,1) 1 1/16
(1,2),(2,1),(2,2) 2 3/16
(1,3),(2,3),(3,1),(3,2),(3,3) 3 5/16
(1,4),(3,4) ,(2,4),(4,1),(4,2),(4,3),(4,4) 4 7/16
Using the probability formula
![P(E)=\frac{Favorable\;outcomes}{Total\;number\;of\;outcomes}](https://tex.z-dn.net/?f=P%28E%29%3D%5Cfrac%7BFavorable%5C%3Boutcomes%7D%7BTotal%5C%3Bnumber%5C%3Bof%5C%3Boutcomes%7D)
Now,
![E(X)=\sum_{i=1}^{n}x_iP(x_i)](https://tex.z-dn.net/?f=E%28X%29%3D%5Csum_%7Bi%3D1%7D%5E%7Bn%7Dx_iP%28x_i%29)
![E(x)=1(1/16)+2(3/16)+3(5/16)+4(7/16)](https://tex.z-dn.net/?f=E%28x%29%3D1%281%2F16%29%2B2%283%2F16%29%2B3%285%2F16%29%2B4%287%2F16%29)
![E(x)=\frac{1+6+15+28}{16}](https://tex.z-dn.net/?f=E%28x%29%3D%5Cfrac%7B1%2B6%2B15%2B28%7D%7B16%7D)
![E(x)=\frac{50}{16}=3.125](https://tex.z-dn.net/?f=E%28x%29%3D%5Cfrac%7B50%7D%7B16%7D%3D3.125)