C consider an unfair six sided die where the probability of...

c) Consider an unfair six-sided die where the probability of rolling a "1" is three times the probability of rolling any other value. All other values have the same probability of occurring. Let X be the random variable that takes on values 1 through 6 for our unfair die. Plot the pmf and CDF of X. Determine the mean of X. EV (10 marks)

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

00:04 Now let me bring up your question here.

00:07 In the question here, we go into play with the unfair six -sided die.

00:15 And the probability of running one will be three times the other values.

00:22 And the others will be the same probability.

00:25 When you plot the pmf, cdf on the x, determine the mean of the x.

00:30 Now let me try to find the value of the x and the probability of the x here.

00:38 X has a value 1, 2, 3, 4, 5 and the 6.

00:50 So the probability of the x because one word curse 3 times more than the others.

01:00 So i will call the others will be the c for now.

01:04 That will be the probability for the others.

01:06 So for c must be the 3c.

01:09 We know that the total probability it must equal to 1.

01:15 When we add up everything here, we have the 8c and it must equal to 1.

01:21 Therefore, c must equal to 1 out of 8.

01:24 And then we can rewrite this probability will be the 3 out of 8, 1 out of 8, 1 out of 8, 1 out of 8, 1 out of 8, 1 out of 8, 1 out of 8.

01:37 And 1 out of 8 and then from here we should be able to compute the eum the x next we need to compute the x times perp of the x if we do that we will multiply by the row here so if we do that we have the 3 out of 8 2 out of 8 3 out of 8 4 out of 8 5 out of 8 and 6 out of 8 now again we will compute the total so we have common denominator, there will be 8, then we have 3 plus 2, plus 3 plus 4, plus 5 plus 6.

02:19 And if we compute it, we get equal to the 10, 10, and then 20, 23 over 8...

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