00:01
Hi, so we are given that the function f of x is equals to 2x minus 1 by 16 with the random variable of x 1 2 3 and 4 in the a part we need to find the probability that x is at most superstable.
00:26
Let us calculate the required values of probability when x is equals to 1 2 3 and 4.
00:33
So at x is equals to 1 clearly p of 1 should be equals to 2 into l of x is 1 minus of 1 divided by 16 will comes out equals to 1 by 16 at x is equals to 2 we get the required probability as p of 2.
00:48
So that will be gives to the 2 2 the 4 minus of 1 by 16 that will comes out equals to 3 by 16 here.
00:57
Similarly at x is equals to 3 you are going to get required probability of p of 3 is equals to 2 into 3 minus 1 by 16 will comes out equals to 5 by 16 here.
01:09
Similarly at x is equals to 4 you will get p of 4 this will be gives to 2 multiplied by 4 minus 1 by 16 will be equals to 4 to that minus 1 7 by 16 here in the similar way.
01:24
So basically our required probability distribution is x as 1 2 3 and 4 we were got p of x as 1 over 16 3 by 16 then 5 by 16 and 7 by 16.
01:43
So basically in the a part we have to find the probability for at most 2.
01:51
So this can be equals to so at most 2 this will be what the probability of getting x is equals to 1 plus probability of getting x is equals to 2 because at most 2 we have to find it out.
02:04
So this should be equals to 1 over 16 plus 3 by 16 taking common so 3 plus 1 will become 4 over 16.
02:14
So 4 plus 16 that means it will comes out equals to 1 by.
02:17
So this is going to be the required answer for a part of this question.
02:22
Now in the b part we have asked to find expected value of x whose formula can be given by e of x is equals to the summation of x value to that of probability value.
02:36
So we just have to vary its value from 1 to 4 as it is varying.
02:41
So the first value is 1 multiplied by its required probability we have been found in table 1 by 16 plus the second value multiplied by its probability of happening 3 by 16 plus the third value its probability is 5 by 16 plus the fourth value 4 multiplied by the 7 by 16.
03:00
So after simplifying and solving the expected value will comes out 15 by 16...