A mail order computer business has six telephone lines let x...

A mail-order computer business has six telephone lines. Let X denote the number of lines in use at a specified time. Suppose the pmf of X is as given in the accompanying table. x 0 1 2 3 4 5 6 p(x) 0.10 0.15 0.20 0.25 0.20 0.08 0.02 Calculate the cdf F(x). x 0 1 2 3 4 5 6 F(x) Graph the cdf F(x). Use the graph to calculate the probabilities of the events given below. (a) {at most three lines are in use} (b) {fewer than three lines are in use} (c) {at least three lines are in use} (d) {between two and five lines, inclusive, are in use}

Transcript

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

00:03 Now let me bring up your question here.

00:06 In the question here, we want to formulate the density function and the cumulative density function for the random variable x.

00:15 So let me draw the table here.

00:21 The first one will be the x, then this one will be the probability of the x, and then we have the cumulative of the x.

00:31 Now x can take the value of 0, 1, 2, 3, 4, 5 and the 6.

00:39 Now we are given the probability for the x equal to the 0 .10, 0 .15, 0 .20, 0 .20, 0 .20, 0 .08, and 0 .02.

00:55 And for the cumulative, we will add up from the beginning.

00:59 So we start with the 0 .20.

01:01 The next one will end up the first and second, and then we add them up, we get equal to the 75.

01:07 The next one will end up to the three values.

01:10 Then we get equal to the 0 .45.

01:12 So we keep adding up because that will be the cumulative.

01:15 Therefore, this one will get equal to the 770.

01:18 And this one will be the 0 .9.

01:21 And this one equal to the 0 .98.

01:26 And so this one will be the 0 .02 here.

01:30 And the last one will be excel.

01:31 Equal to the 1.

01:32 And that's going to be the answer for the part 1.

01:35 And then the next one you need to graph the cdf on the x.

01:43 So we will have, let's say this one will be the 0, 1, and this will be the 2, 3, 4, 5, and the 6.

01:54 Now we have the, for the 0, it will equal to the 0 .1.

02:01 So maybe i will bring this down a little because i don't have enough space.

02:05 Here so i will have this one and this have a zero one two three four five and the six so the first one it will have the probability equal to z -1 one so let's say this one will be the zapon one and you will have and this will be the full dot and then we go to this one will be the empty dot and so before the 0 it will be equal to the 0 here and up to the 1 this one will be the empty dot and then when we have under 0 we get equal to the 0 .1 so this will be the full dot then we go here will be the empty after that will be the 2 .5 so this will be the 2 .5 and it will be the full dot and then go to this and empty and then then from the 2, it will get 0 .45, this 3, 4, 4 .5.

03:15 0 .4 .5.

03:15 This one will be the 0 .4 .5.

03:18 It will be the 0 .25.

03:22 So this one will be the full dot here...

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