This post covers Introduction to probability from Statistics for Engineers and Scientists by William Navidi.

Exercises

• A data center contains $1000$ computer servers. Each server has probability $0.003$ of failing on a given day.

  a. What is the probability that exactly two servers fail?

  b. What is the probability that fewer than $998$ servers function?

  c. What is the mean number of servers that fail?

  d. What is the standard deviation of the number of servers that fail?

Solution: (a) 0.2240 (b) 0.5768 (c) 3 (d) 1.732

• The number of hits on a certain website follows Poisson distribution with a mean rate of $4$ per minute.

a. What is the probability that $5$ hits are received in a given minute?

b. What is the probability that $9$ hits are received in $1.5$ minutes?

c. What is the probability that fewer than $3$ hits are received in a period of $30$ seconds?

Solution: (a) 0.1563 (b) 0.0688 (c) 0.6767