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Q 3 . Just part a ) Q 4 . Part a and b Suppose that, for - 1 1 , the random variables x
Q Just part a
Q Part a and b
Suppose that, for the random variables and have the joint probability
density function given by
a Prove that the function is indeed a joint probability density function for
all
b Show that the marginal distributions of and are both exponential distribu
tions with mean
c Show that and are independent if and only if
d Find the covariance Cov of and
e Show that Cov if and only if
points
Suppose that is a binomial random variable based on Bernoulli trials with success
probability and consider the random variable defined by
a Prove that for dots, we have
b Use the result in a to find the probability distribution of the random variable
and specify its parameters.
c The probability that a patient recovers from a rare blood disease is If
people are known to have contracted this disease, what is the probability that
at least survive,
from to survive, and
exactly survive?
Hint: Use Appendix Table A in the textbook!
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