On average, a particular web page is accessed 10 times an hour. Let X be the...
On average, a particular web page is accessed 10 times an hour.
Let X be the number of times this web
page will be accessed in the next hour.
(a) What is E[X] and Var[X]?
(b) What is the probability there is at least one access in the
next hour?
(c) What is the probability there are between 8 and 12 (inclusive)
accesses in the next hour?
and,
Let X be a random variable with image Im(X) = (0, 1, 2, 3)
x 0 1 2 3
pX(x) 0.05 0.25 0.1 0.15
(d) Let Y be a random variable with Y = 5 + 2X where X has the pmf from above;
i. Determine the image of Y .
ii. Using the rules for computing expected values and variances of
a linear function of a random variable, find the expected value and
variance of Y .
(e) Suppose we have a collection of independent and identically
distributed Xi according to above the table and Z = 
, (the answer will depend on
n).
i. What is E[Z]?
ii. What is Var[Z]?
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On average, a particular web page is accessed 10 times an hour.
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