The first question:
Expected return =-2× 0.99+(50-2 )× 0.01=-1.5.
The second question:
The expected income of single lottery =-2× 0.9329+(14.9-2 )× 0.0671=-1.00021.
Expected value of 10 Note =10×-1.0001=-10.5438+0.
The third question:
The expected income of single-note lottery = -5×0.98+(50-5)×0.02 = -4.
2 note that expected value =2× -4 = -8.
The fourth question:
* * * There are 3×3=9 throwing methods.
The number of letters in mailbox A is 0, and there are 2×2=4 ways to send letters.
The letter number of mailbox A is 1, and there are 2×2=4 voting methods.
When the number of letters is 2, there are 1 ways to throw out the letters in mailbox A.
eζ= 0×4/9+ 1×4/9+2× 1/9 = 6/9
The fifth question:
The probability of zeta = 2 is 0.9.
The probability of zeta =1is 0. 1×0.9=0.09.
The probability of zeta = 0 is1-0.1-0.09 = 0.01.
eζ= 2×0.9+ 1×0.09+0×0.0 1 = 1.89