There are two envelopes, each of which has a check for a unif(0,1) amount of money, measured in thousands of dollars. the amounts in the two envelopes are independent. you get to choose an envelope and open it, and then you can either keep that amount or switch to the other envelope and get whatever amount is in that envelope.
suppose that you use the following strategy: choose an envelope and open it. if you observe 'u', then stick with that envelope with probability 'u', and switch to the other envelope with probability 1-u
a) find the probability that you get the larger of the two amounts
b) find the expected value of what you will receive

What two criteria are needed for triangles to be similar

The difference between two numbers is one. three times the larger number minus two times the smaller number is 9. what are the two numbers

Each of the following data sets has a mean of x = 10. (i) 8 9 10 11 12 (ii) 7 9 10 11 13 (iii) 7 8 10 12 13 (a) without doing any computations, order the data sets according to increasing value of standard deviations. (i), (iii), (ii) (ii), (i), (iii) (iii), (i), (ii) (iii), (ii), (i) (i), (ii), (iii) (ii), (iii), (i) (b) why do you expect the difference in standard deviations between data sets (i) and (ii) to be greater than the difference in standard deviations between data sets (ii) and (iii)? hint: consider how much the data in the respective sets differ from the mean. the data change between data sets (i) and (ii) increased the squared difference îł(x - x)2 by more than data sets (ii) and (iii). the data change between data sets (ii) and (iii) increased the squared difference îł(x - x)2 by more than data sets (i) and (ii). the data change between data sets (i) and (ii) decreased the squared difference îł(x - x)2 by more than data sets (ii) and (iii). none of the above