Questions from Engineering Statistics

Q: Suppose that there are n trials x1, x2, . .

Suppose that there are n trials x1, x2, . . . , xn from a Bernoulli process with parameter p, the probability of a success. That is, the probability of r successes is given by Work out the maximum...

Q: Consider the lognormal distribution with the density function given in Section 6

Consider the lognormal distribution with the density function given in Section 6.9. Suppose we have a random sample x1, x2, . . . , xn from a lognormal distribution. (a) Write out the likelihood func...

Q: Consider a random sample of x1, . . . , xn

Consider a random sample of x1, . . . , xn coming from the gamma distribution discussed in Section 6.6. Suppose the parameter α is known, say 5, and determine the maximum likelihood estimation for par...

Q: Consider a random sample of x1, x2, . . .

Consider a random sample of x1, x2, . . . , xn observations from a Weibull distribution with parameters α and β and density function / (a) Write out the likelihood function. (b) Write out the equ...

Q: Consider a random sample of x1, . . . , xn

Consider a random sample of x1, . . . , xn from a uniform distribution U(0, θ) with unknown parameter θ, where θ > 0. Determine the maximum likelihood estimator of θ.

Q: Consider the independent observations x1, x2, . . . ,

Consider the independent observations x1, x2, . . . , xn from the gamma distribution discussed in Section 6.6. (a) Write out the likelihood function. (b) Write out a set of equations that, when solve...

Q: Consider a hypothetical experiment where a man with a fungus uses an

Consider a hypothetical experiment where a man with a fungus uses an antifungal drug and is cured. Consider this, then, a sample of one from a Bernoulli distribution with probability function where...

Q: Consider the observation X from the negative binomial distribution given in Section

Consider the observation X from the negative binomial distribution given in Section 5.4. Find the maximum likelihood estimator for p, assuming k is known.

Q: Consider two estimators of σ2 for a sample x1, x2,

Consider two estimators of σ2 for a sample x1, x2, . . . , xn, which is drawn from a normal distribution with mean μ and variance σ2. The estimators are the unbiase...

Q: Regular consumption of presweetened cereals contributes to tooth decay, heart disease

Regular consumption of presweetened cereals contributes to tooth decay, heart disease, and other degenerative diseases, according to studies conducted by Dr. W. H. Bowen of the National Institute of H...