0:00
Hello students.
00:02
So we have given this probability distribution for random variable x and now first we have to find the value of a value of k.
00:11
So we know that summation of f of x is equal to 1 when it is a probability distribution.
00:19
So we can write it is equal to k plus 3k plus 4k plus 2k is equal to 1 and and this is equal to 10k is equal to 1.
00:35
That means k is equal to 1 by 10.
00:39
So k is equal to 1 by 10.
00:43
Now we have to find the expectation of x.
00:46
So we know the formula for expectation of x is, expectation of x is equal to summation of x into p of x.
00:57
So now put the values that is 0 into 0.
01:02
K plus 1 into 1 into 3k that means 3k that means 1 by 10 okay we will put the value of k in the next step so 1 into 3k plus next is 2 into 4k plus 3 into 2k now this is equal to 17 k and now 17 into k is 17 into k is is 1 by 10 so that means this is equal to 1 .7 so expectation of x is 1 .7 then next we have to find the median and for that so first we will find here probability of x is less than equal to 1 is equal to less than or equal to 1 that means 0 and 1 the probability of 0 plus 1 that means k plus 3 k which is equal to 4k, that means 4 into 1 by 10, that is 0 .4, and this is less than 0 .5.
02:16
Then next, we know that probability of x less than equal to 2, and this is equal to k plus 3k plus 4k, which is equal to 0 .8...