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Question 1: The CDF of a discrete random variable X is given below. egin{equation} F(x) = egin{cases} 0, & ext{for } x < 0, \ frac{1}{16}, & ext{for } 0 le x < 1, \ frac{5}{16}, & ext{for } 1 le x < 2, \ frac{11}{16}, & ext{for } 2 le x < 3, \ frac{15}{16}, & ext{for } 3 le x < 4, \ 1 & ext{for } x ge 4. end{cases} end{equation} (a) Find and sketch the PMF of the random variable. (b) Evaluate the probability $P[Xge 1 | X le 4]$

          Question 1:
The CDF of a discrete random variable X is given below.
egin{equation*}
F(x) = egin{cases}
0, & 	ext{for } x < 0, \
frac{1}{16}, & 	ext{for } 0 le x < 1, \
frac{5}{16}, & 	ext{for } 1 le x < 2, \
frac{11}{16}, & 	ext{for } 2 le x < 3, \
frac{15}{16}, & 	ext{for } 3 le x < 4, \
1 & 	ext{for } x ge 4.
end{cases}
end{equation*}
(a) Find and sketch the PMF of the random variable.
(b) Evaluate the probability $P[Xge 1 | X le 4]$

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$Question 1: The CDF of a discrete random variable X is given below. eginequation* F(x) = egincases 0, extfor x < 0, frac116, extfor 0 le x < 1, frac516, extfor 1 le x < 2, frac1116, extfor 2 le x < 3, frac1516, extfor 3 le x < 4, 1 extfor x ge 4. endcases endequation* (a) Find and sketch the PMF of the random variable. (b) Evaluate the probability P[Xge 1 | X le 4]$

Added by Lauren K.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert David Nguyen

10/31/2021

Step 1

However, since the CDF is not provided in the question, we cannot directly find the PMF. Generally, the PMF is found by subtracting the value of the CDF at a point from the value of the CDF at the next point. Show more…

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Question 1: The CDF of a discrete random variable X is given below. F(x) = 0, for x < 0, 1/16, for 0 <= x < 1, 5/16, for 1 <= x < 2, 11/16, for 2 <= x < 3, 15/16, for 3 <= x < 4, 1 for x >= 4. (a) Find and sketch the PMF of the random variable. (b) Evaluate the probability P[X >= 1 | X <= 4]

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Transcript

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

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

00:08 In this question we're given the cdf of the random variable x and then let me try to raise down here for you.

00:17 We have the f x equal to 2.

00:21 So equal to 0 if the x smaller than 0 equals 1 over 16 if x small equals 0 is smaller than 1, 5 over 16 if x smaller equal 0 is smaller than 1, 5 over 16, if x between the 1 and 2 and 11 over 16 if x between the 2 and the 3 15 over 16 if we have x between the 3 and the 4 equal to 1 if x greater equal to 4 now the question i asked let you sketch the bmf on the random variable so let me sketch it on the right here for you so i will have here will be the x value will be from 0 1, 2, 3, and 4.

01:13 And this one over 16, so let me think this one will be 1 here.

01:17 So this one will be the 0 .5.

01:21 And then it means that this one will be the 8 out of 16.

01:29 This will be 4 out of 16.

01:32 This will be the 12 out of 16.

01:37 So when x smaller than 10.

01:39 And zero we have, this will be zero here.

01:42 After that we have found the x between 0 and 1.

01:47 This will be the empty here for now.

01:50 After from 0 to 1, we have 1 over 16.

01:53 So 1 over 16 will be here.

01:55 This will be the full dot.

01:57 Then we go here, empty dot...

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