00:01
Hello students, today we will discuss about this question.
00:04
In this question we are given that consider some special four -sided dice.
00:10
Four -sided dice, roll two of these dice and let x denote the minimum of two values that appears and let y denotes the maximum of two values that appear.
00:31
Now here we need to find the expected value of x so therefore e of x is equals to question mark and we need to find the expected value of y that is e of y is equals to question mark so here first of all there is total four outcomes when a four dice is rolled that is one two three and four now when two dice that are rolled together there is a total four multiplied by four outcomes so therefore here we can say total outcomes that is equals to 4 multiplied by 4 that is 16.
01:09
And these outcomes that are 1 -1, 1 -2, 1 -3, 1 -4, 2 -1, 2 -2, 2 -2, 2 -3, 24, then 3 -1, 3 -3, 3 -4, 4 -1, 4 -2, and 4 -4.
01:36
Now, outcome where 1, 1, 2, 3, 3, 4 have considered here that the outcome is not considered here, that outcome is same on the 2 dice.
01:50
So therefore, the probability distribution for the x, that is x, p of x, is equal to 1, 2, 3, and 4, that is 6 divide by 16, 4 divide by 16, 2 divide by 16, and 0.
02:04
And here, so therefore the expected value of e of x, that can be given as summation of xi, p of xi, so that is equals to 1 multiplied by 6 divided by 16 plus 2 multiplied by 4 divided by 16 plus 3 multiplied by 2 divided by 16 plus 4 multiplied by 0 is equals to 1 .25...
