Neatly hand write your solutions - marks will be assigned for presentation
Let X be a random variable with mean µ = 4 and variance σ2 = 8. What is E(2X2)?
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?
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) =
(a) Compute the value of c in the pdf .
c(x2 − 1) 1 ≤ x < 3
otherwise
Compute the probability X is between 1.5 and 2.25 inclusive.
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?
The thickness measurements of glass sheets produced by a certain process are normally dis-tributed 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)?
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.
