# Thread: expected value

1. ## expected value

X is a random variable that represents the number of telephone lines in useby the technical support center of a software manufacturer at noon each day. The prob. distribution of X is show below

x 0 1 2 3 4 5
p(x) .35 .2 .15 .15 .10 .05

1. Calculate the expected value (the mean) of X.

(0)(.35)+(1)(.20)+(2)(.15)+(3)(.15)+..... = 1.6

2. Using past records, the staff at the technical support center randomly selected 20 days and found that an average of 1.25 telephone lines were in use at noon on those days. The staff proposes to select another random sample of 1,000 days and computer the average number of telephone lines that were in use at noon on those days. How do you expect the average from this new sample to compare to that of the first sample? Explain

3. Picture ( I had to add an attachment because i don't know how to make signs)

4. describe the relationship between the mean and the median relative to the shape of the distribution

This is as far as I have gotten, Not sure what to do next. That is if my first part is right.

2. Originally Posted by Airjunkie
X is a random variable that represents the number of telephone lines in useby the technical support center of a software manufacturer at noon each day. The prob. distribution of X is show below

x 0 1 2 3 4 5
p(x) .35 .2 .15 .15 .10 .05

1. Calculate the expected value (the mean) of X.

(0)(.35)+(1)(.20)+(2)(.15)+(3)(.15)+..... = 1.6

2. Using past records, the staff at the technical support center randomly selected 20 days and found that an average of 1.25 telephone lines were in use at noon on those days. The staff proposes to select another random sample of 1,000 days and computer the average number of telephone lines that were in use at noon on those days. How do you expect the average from this new sample to compare to that of the first sample? Explain
You would expect the avaerage of the larger sample to be closer to the mean number of lines. In fact calculating the SE of means of samples of size 1000, we would expect such a sample mean to be between about 1.5 and 1.7.

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3. Originally Posted by Airjunkie
X is a random variable that represents the number of telephone lines in useby the technical support center of a software manufacturer at noon each day. The prob. distribution of X is show below

x 0 1 2 3 4 5
p(x) .35 .2 .15 .15 .10 .05

3. Picture ( I had to add an attachment because i don't know how to make signs)
The condition p(X<=x)>=0.5 is satisfied by any x>=1 and p(X>=x)>=0.5 by x<=1. Hence they are satisfied simultaneously by x=1.

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4. Constantine, so the probability distribution is just 1?