The discrete random variable X can take only the values 1, 2...

The discrete random variable X can take only the values 1, 2 and 3. For these values the cumulative distribution function is defined by F(x) = (x^3 + k) / 40 x = 1, 2, 3 (a) Show that k = 13 (b) Find the probability distribution of X. Given that Var(X) = 259 / 320 (c) find the exact value of Var(4X - 5).

Transcript

00:01 Hi, i'm david and i'm here to help you answer your question.

00:03 Let me bring up your question here.

00:06 In this question we are given the cumulative distribution function and then from there we need to find the missing value case and then we have to find the pdf of the function as well.

00:20 Now i remind you that in a to be considered as a cumulative distribution function, the f of the maximum value here will be the 3, it must exact equal to 1.

00:36 So means that when we blake in the own value here and then we must have it equal to the equal to 1.

00:46 Therefore when we put it in in the part 8, once you find the f of the 3, it must equal to the 3 -border 3 plus k over 40.

01:00 And it will simplify this one we have equal to the 27 plus k over 40 and this one must equal to the one so from here we will see that the 27 plus k must equal to the 40 therefore k will equal to the 40 minus 27 and it will equal to the 13 so we only approved that the k must equal to the 13 in the part now in the part b, want to find the probability distribution on the x.

01:38 So means then we have to find the f on the 1 and f on the 2 and f on the 3.

01:49 Remind to you that the cumulative distribution function is equal to the probability then the x -money equals to the small x.

01:58 Therefore the f of the 1 will mean the standing value on the x, therefore just exactly equal to the f of the one, the capital one.

02:07 So if we put the one inside, we have the one power three.

02:11 We found the k equal to the 13 over 40...

Question

Please give Ace some feedback