The following table shows the density of the random variable...

The following table shows the density of the random variable X. egin{tabular}{|c|c|c|c|c|c|c|c|} hline $x$ & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \ hline $p(x)$ & 0.03 & 0.01 & 0.04 & 0.3 & 0.3 & 0.1 & 0.07 & ? \ hline end{tabular} (a) Find $p(8)$? (b) Find the table for CDF $F(x)$? (c) Find $P(3 le X le 5)$ (d) Find $P(X le 4)$ and $P(X < 4)$. are the probabilities the same? (e) Find $F(-3)$ and $F(10)$

Transcript

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

00:03 Now in this question we are given the table of the probability distribution, so let me write down again here for you.

00:10 We have the x and the probability in the x.

00:15 X has a value of the 1, 2, 3, 4, 5, 6, 7 and the 8.

00:25 And the corresponding probability equal to the 0 .0 3, 0 ,000, 0 .0 .0 .0 .0 .0 .0 .0 .0 .0.

00:35 0 .0.

00:36 0.

00:37 0.

00:39 And we want to find the probability in part a, the probability of the x equal to 8.

00:47 Here, it's just equal to the 1 minus 0 on of the others.

00:51 So we have 0 .03 plus 0 .0 .0 1, plus 0 .04, plus 0 .03, plus 0 .0 .3, plus 0.

01:00 Plus 0 .1 plus 0 .07.

01:03 If we do the calculation here, 0 .03 plus 0 .0 .0 .0 .4 plus 0 .3 plus 0 .3 plus 0 .0 .7.

01:17 1 minus that can equal to the 0 .05.

01:22 So that will be the answer for the a.

01:25 Now for the b, once you find the cdf.

01:30 You find the cdf it will be just a cumulative distribution so we have here x and then the px here so one two three four five six seven and the eight for the first one will be the same thing like zero pon zero three for the two we will end up the first two so got the zero point zero four for the three will end up the first three so again equal to 0 .08.

02:01 And for the 4 we will add plus the 0 .3, we got the 0 .33.

02:06 For the 5, we add more with the 5, we got the 0 .68.

02:11 For the 6, we add extra 0 .1, got 0 .78...

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