D. Let X be a random variable with pdf f(x) = c(x+2), x =...

D. Let X be a random variable with pdf $f(x) = c(x+2)$, $x = -1, 0, 1, 2$, where c is some number. (16) The number c is (a) 1/10 (b) 1/8 (c) 1/6 (d) 1/4 (17) $P(X \ge 1)$ is (a) 3/10 (b) 7/10 (c) 7/8 (d) 13/8 (18) The mean of X is (a) -1 (b) 0 (c) 1 (d) 2 (19) The variance of X is (a) 0 (b) 1 (c) 2 (d) 3 (20) $E[X/(X+2)]$ is (a) 1/10 (b) 2/10 (c) 5/8 (d) 7/8

Transcript

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

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

00:06 In the question here, we are given the density on the random variable x on the form equal to 1 out of 8 for the x inside the interval from the 1 and the 9.

00:17 Remember this one is just equal to the uniform distribution.

00:22 Now it will try to draw the graph on the uniform distribution.

00:26 It will have something like this.

00:28 So let's say 1 here and the 9 here and then the graph will be something like this form where we have the height from here to here equal to the 1 over 8.

00:43 Now the first question asked in the question a, once you find the probability of the x, it will be between the 1 and the 5.

00:53 To find this probability that equal to 1, let's say 5 will be somewhere here.

00:58 Then the probability just equal to the area here and the area there just equal to the base with times in the height and the base equal to the 5 minus 1 times of the height equal to 1 over 8 equals to 4 over 8 and equal to 0 .5 then find the answer for the first part equal to the p for the part b want to find the probability that the x will be between the 3 and 3 and the 8.

01:33 So let's say 3 will be somewhere here and 8 will be here.

01:37 Then the probability we're looking for equal to this area.

01:40 So again, equal to the area, equal to the base equal to the 8 minus 3.

01:46 The height equal to 1 out of 8, equal to 5 out of 8...

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