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# Stat261 Assignment #1

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Stat261
Assignment #1
Neatly hand write your solutions – marks will be assigned for presentation
1. Let X be a random variable with mean µ = 4 and variance σ
2 = 8. What is E(2X2
)?
2. In November of each year, a walk-in clinic allows people to walk in to get a flu shot. Let X
be the number of people who come to the clinic for a flu shot on a randomly selected day (in
November). Suppose X has the following distribution:
x 0 1 2 3 4 5
P(X = x) 0.3 0.2 0.2 0.1 0.1 0.1
If at least 2 people walk in for a flu shot on a particular day, what is the probability that there
are 4 or fewer who walk in for a flu shot that day?
3. You want to read a disk sector from a 7200rpm disk drive. Let T be the time you wait, in
milliseconds, after the disk head is positioned over the correct track, until the desired sector
rotates under the head. The random variable T has the following probability density function
(pdf),
f(x) = (
c(x
2 − 1) 1 ≤ x < 3
0 otherwise
(a) Compute the value of c in the pdf.
(b) Compute the probability X is between 1.5 and 2.25 inclusive.
4. Assume a page in the book will be considered defective if there are more than 3 typos on the
page. On average, on one page there is 1 typo. Let X denote the number of typos on one page
and assume that it has a Poisson distribution. What is the probability that a randomly chosen
page is defective?
5. The thickness measurements of glass sheets produced by a certain process are normally distributed with a mean of µ = 3.00 mm and a standard deviation of σ = 0.12 mm. What is the
value of c for which there is a 99% probability that a glass sheet has a thickness measurement
within the interval (3.00-c, 3.00+c)?
6. Daily sales at a gas station are thought to be independent of one another with daily mean \$5250
and standard deviation \$700. Approximate the probability that the average daily sales over one
year (i.e. 365 days) is greater than \$6,000. Stat261 Assignment #1
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