In the Advanced Placement (AP) programs of high schools, during the senior year 40% of students study subject D, 45% study subject E, and 50% study subject F. It is also known that 10% study both subjects D and F, 20% study both subjects E and F, 15% study subject D but neither subject E nor F. Only 5% of the students study all three subjects.

(a) Define the random variable X as the number subjects taken (out of D, E, and F) by AP students during the senior year. Obtain the probability mass function and cumulative distribution function of X and represent it in the tabular form.

(b) Obtain the expected value of X.

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a To define the random variable X find the probabilities for each possible value of X 0 1 2 and 3 ba... View the full answer