Determine the cumulative distribution function of a binomial random variable with n=3 and p=1/4.

When a computer disk manufacturer tests a disk, it writes to the disk and then tests it using a certifier. The certifier counts the number of missing pulses or errors. The number of errors on a test area on a disk has a Poisson distribution with λ = 0.2. a. What is the expected number of errors per test area? b.

Suppose that X has a Poisson distribution with a mean of 4. Determine the following probabilities: a. P(X = 0) b. P(X ≤ 2) c. P(X = 4) d. P(X = 8)

An electronic product contains 40 integrated circuits. The probability that any integrated circuit is defective is 0.01 , and the integrated circuits are independent. The product operates only if there are no defective integrated circuits. What is the probability that the product operates?

Sketch the probability mass function of a binomial distribution with n = 10 and p = 0.01 and comment on the shape of the distribution. a. What value of X is most likely? b. What value of X is least likely?

In a semiconductor manufacturing process, three wafers from a lot are tested. Each wafer is classified as pass or fail. Assume that the probability that a wafer passes the test is 0.8 and that wafers are independent. Determine the probability mass function of the number of wafers from a lot that pass the test.

Suppose that the number of customers who enter a store in an hour is a Poisson random variable, and suppose that P(X=0)=0.05. Determine the mean and variance of X.

There were 49.7 million people with some type of long-lasting condition or disability living in the United States in 2000. This represented 19.3 percent of the majority of civilians aged five and over (http://factfinder.census.gov). A sample of 1000 persons is selected at random. a. Approximate the probability that more than 200 persons in the sample have a disability. b. Approximate the probability that between 180 and 300 people in the sample have a disability.

If the last digit of a weight measurement is equally likely to be any of the digits 0 through 9, a. What is the probability that the last digit is 0? b. What is the probability that the last digit is greater than or equal to 5?

Batches that consist of 50 coil springs from a production process are checked for conformance to customer requirements. The mean number of nonconforming coil springs in a batch is five. Assume that the number of nonconforming springs in a batch, denoted as X, is a binomial random variable. a. What are n and p? b. What is P(X ≤ 2)? c. What is P(X ≥ 49)?

Product codes of two, three, four, or five letters are equally likely. What are the mean and standard deviation of the number of letters in the codes?

Suppose that X has a Poisson distribution with a mean of 64. Approximate the following probabilities: a. P(X > 72) b. P(X < 64) c. P(60 < X ≤ 68)

In a NiCd battery, a fully charged cell is composed of nickelic hydroxide. Nickel is an element that has multiple oxidation states. Assume the following proportions of the states:

$$\begin{array}{cc}\text { Nickel Charge } & \text { Proportions Found } \\ 0 & 0.17 \\ +2 & 0.35 \\ +3 & 0.33 \\ +4 & 0.15\end{array}$$

Determine the mean and variance of the nickel charge.

Assume that the number of errors along a magnetic recording surface is a Poisson random variable with a mean of one error every

$$10^5$$

bits. A sector of data consists of 4096 eight-bit bytes. a. What is the probability of more than one error in a sector? b. What is the mean number of sectors until an error occurs?