A person's white blood cell (WBC) count W (measured in thousands of cells per microliter of blood) and body temperature T (in degrees Celsius) can be mode led as bivariate Gaussian random variable such that IV is Gaussian (7, 2) and T is Gaussian (37, 1). To determine whether a person is sick, first the person's temperature T is measured. If T> 38, then the person's WBC count is measured. If 14' > 10. the person is declared ill (event I).
(a) Suppose W and T are uncorrelated. What is P[IJ? Hint: Draw a tree diagram for the experiment.
(b) Now suppose W and T have correlate ion coefficient PW,T = 1/√2. Find the conditional probability P[I\T = t] that a person is declared ill given that the person's temperature is T = t.