Statistical Modeling - Assignment (Due date: Oct 9th, 2018)
NO MARK will be given for late submission.
1) Let X be the hospital period (in days) for patients following treatment for a certain type of kidney
disorder, which is a random variable with probability mass function
f(x) = p(1 p)x 1; x = 1;2;3;::::
(a) Find the moment generating function of X;
(b) Find the mean and the variance of X:
2) Let X1;X2;:::;Xn be a random sample of size n from a normal distribution N( ; 2): Show that
cS is unbiased estimator of , where
c =rn 12n 12 n2 !:
3) The breaking strength X of a certain rivet used in a machine engine has a mean 5000 psi and
standard deviation 400 psi. Find the minimum sample size to have
P(4900 10 33 21
At = 0:05; perform. an appropriate test to determine if the proportions of widows and widowers
are di erent with respect to the di erent time periods that a spouse survives after the death of his
or her mate.
9) This data set (cooking.csv) contains cooking time, level of oven, and ue temperature for 10
observations. It is of interest to predict cooking time a particular level of oven and ue temperature.
(a) Fit a multiple linear regression equation of the form
y = a0 +a1x1 +a2x2:
(b) Predict the cooking time at level of oven of 5.5 and ue temperature of 20.
(c) Is there a relationship between cooking time and ue temperature? (Use = 0:05)