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.

Sale!