00:01
So, first we have to find the probability of each possible outcome.
00:04
Since x has a discrete uniform distribution on the integers where x belongs from 4 to 7, there are 4 possible outcomes being 4, 5, 6 and 7.
00:22
Each outcome has an equal probability of occurring.
00:27
So, we can find the probability of each outcome by dividing 1 by the number of outcomes.
00:32
So, probability of x equals to 4 would be equal to probability of x equals to 5 which would be equal to probability of x equals to 6 which would be equal to the probability of x equals to 7.
00:48
All of them are equal to 1 divided by 4.
00:54
Now, finding the mean.
00:55
The mean or expected value of x is given by the formula u equals to e of x which is equal to summation of x of p of x where summation of x means the sum of all possible values of x.
01:19
In this case, u would be equal to e of x which would be equal to 4 times 1 divided by 4 plus 5 times 1 divided by 4 plus 6 times 1 divided by 4 and plus 7 times 1 divided by 4.
01:44
So, this would be equal to 5 .5...