The probability mass function of a discrete random variable...

The probability mass function of a discrete random variable X is given by: P(x) = { x/10, if x = 1, 2, 3, 4; 0, otherwise a. Draw the probability mass function (PMF) of this random variable. b. Draw the cumulative distribution function (CDF) of this random variable. c. What is the Prob(2 < X ? 4)? Write it in terms of the CDF. d. What is E[X]? e. What is Var[X]? f. What is E[X(6-X)]? g. What is Var[3X-2]?

Transcript

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

00:03 In the question here we are given the discrete random rubble x under corresponding probability equal to the x over 10 for the x equal to the 1, 2, 3 and 4 and equal to 0 elsewhere.

00:19 Now in the question a, i'm asking you to draw the probability mass function of the random variable so we can make it here.

00:30 Now suppose this will be the 0 and this will be the 1 and maybe i will put this one will be the this one will be the 1 out of 10 2 out of 10 3 out of 10 and 4 out of 10 so the value of the first value of the 1 and then it will have it will be equal to this one so i will draw the line here and it will be this value the next one will be for the exit to the two so we have one two two three and four and the next one will be equal to the yeah actually to the two will be two out of ten exit to the three will be the three out of ten exit to the four will be the four out of ten and that will be the answer of the part a now for the part b once you draw the cumulative distribution on the cdf, so we'll do it to be here.

01:38 So i want to draw on the cumulative, so i will have to do it larger here.

01:46 So again, this one will be the 1 out of 10.

01:50 And we will have here will be the 1, 2, 3, 4.

01:55 And when x2 1 to 1 will be 1 out of 10 will be here.

02:01 And then when exit to the 2, we end up from the 1 and the 2, we get equal to the 3 out of 10.

02:07 So that will be the 3 out of 10.

02:10 Then it will be here.

02:14 And when x.

02:15 X equal to the 3, we will have 6 out of 10.

02:18 So 6 it will be 1, 2, 3, 4, 5, 6 will be here.

02:25 6 out of 10.

02:26 Then we will have it will be here.

02:29 And the last one, when xing into the 4, it will be the 10 out of 10.

02:33 So which is 1.

02:35 So have a 6 and 10.

02:37 So that will be the 1.

02:38 And then the one we're looking for will be this one and that will be the answer for the b now for the c one to find the probability of the x will be between the 2 and the 4 when run to write this one as a cdf so this one can be written down is a probability of the x small equal to the 4 minus the probability of the x smaller than the 2 and this one here just equal to the f of the 4 that will be the cumulative distribution.

03:11 X smaller than 5, strictly smaller than 2.

03:14 So it can be equal to the x smaller than equal to 1...

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