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In: Statistics and Probability

A child who gets into an elite preschool will have a lifetime earning potential given by...

A child who gets into an elite preschool will have a lifetime earning potential given by a Poisson random variable with mean $3,310,000. If the child does not get into the preschool, her earning potential will be Poisson with mean $2,700,000. Let X = 1 if the child gets into the elite preschool, and zero otherwise, and assume that P(X = 1) = p.

(a) Find the covariance of X and the child’s lifetime earnings.

(b) Find the correlation of X and the child’s lifetime earnings.

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