Question

A loaded S-sided de is loaded so that the number 4 occurs 3/10 of the time while the other numbers occur with equal frequency. What is the expected value of this die? CASS 08.44 OC.48 Next O My

Answer 1

The probablity of obtain a 4 is= 3/10

The probablity of obtain a 1,2,3,5,6,7,8= 1-3/10=7/10

The expect value is:

`E(p)=X1*p1+X2*p2+X3*p3+...+X8*p8`

And p(1)=p(2)=p(3)=p(5)=p(6)=7/10

All have the same frequency, therefore

p(1,2,3,5,6,7,8)=7/10*1/5=7/50=1/10

Where x=1, 2 ,3,4,5,6 and p=3/10 if is 4 and 7/10 for any other number.

Replacing:

`\begin{gathered} E=(1+2+3+5+6)*(7)/(50)+4*(3)/(10) \\ \\ E=2.38+1.2=3.58\approx4 \end{gathered}`