A persons white blood cell wbc count w measured in, Ask an Expert

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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 modeled as bivariate Gaussian random variables such that W 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 W > 10, the person is declared ill (event I)

(a) Suppose W and T are uncorrelated. What is P[I]? Hint: Draw a tree diagram for the experiment.

(b) Now suppose W and T have correlation coeffi- cient ρ = 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.

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