Questions from Engineering Statistics

Q: Let X be a binomial random variable with probability distribution

Let X be a binomial random variable with probability distribution Find the probability distribution of the random variable Y = X2.

Q: The moment-generating function of a certain Poisson random variable X

The moment-generating function of a certain Poisson random variable X is given by MX(t) = e4(et−1). Find P(μ − 2σ

Q: Show that the moment-generating function of the random variable X

Show that the moment-generating function of the random variable X having a chi-squared distribution with v degrees of freedom is MX(t) = (1 − 2t) −v/2.

Q: Using the moment-generating function of Exercise 7.21,

Using the moment-generating function of Exercise 7.21, show that the mean and variance of the chisquared distribution with v degrees of freedom are, respectively, v and 2v. Exercise 7.21: Show that t...

Q: If both X and Y, distributed independently, follow exponential distributions

If both X and Y, distributed independently, follow exponential distributions with mean parameter 1, find the distributions of (a) U = X + Y; (b) V = X/(X + Y ).

Q: A coin is tossed 400 times. Use the normal curve approximation

A coin is tossed 400 times. Use the normal curve approximation to find the probability of obtaining (a) between 185 and 210 heads inclusive; (b) exactly 205 heads; (c) fewer than 176 or more than 227...

Q: A process for manufacturing an electronic component yields items of which 1

A process for manufacturing an electronic component yields items of which 1% are defective. A quality control plan is to select 100 items from the process, and if none are defective, the process conti...

Q: A process yields 10% defective items. If 100 items are

A process yields 10% defective items. If 100 items are randomly selected from the process, what is the probability that the number of defectives (a) exceeds 13? (b) is less than 8?

Q: The probability that a patient recovers from a delicate heart operation is

The probability that a patient recovers from a delicate heart operation is 0.9. Of the next 100 patients having this operation, what is the probability that (a) between 84 and 95 inclusive survive? (b...

Q: A random sample of 12 shearing pins is taken in a study

A random sample of 12 shearing pins is taken in a study of the Rockwell hardness of the pin head. Measurements on the Rockwell hardness are made for each of the 12, yielding an average value of 48.50...