1. (8 points) Consider the probability distribution function for year at school

Question

1. (8 points) Consider the probability distribution function for year at school for undergraduates enrolled in introductor statistics courses at a certain university. (SHOW YOUR WORK)

(a) (2 points) What is the probability that a randomly selected student from this population has been in school at least three years?

(b) (2 points) Find the expected value of the variable X.

(c) (2 points) Explain the meaning of your expected value from part (b) in the context of the situation.

(d) (2 points) Find the standard deviation of the random variable X.

Explanation / Answer

a) P(X > 3 ) = P(X = 3) + P(X = 4)

                   = 0.24 + 0.08 = 0.32

b) E(X) = 1 * 0.08 + 2 * 0.6 + 3 * 0.24 + 4 * 0.08 = 2.32

c) The expected value means the expected no of ungraduates who were enrolled inintroductor statistics classes in the university.

d) E(X^2) = 1^2 * 0.08 + 2^2 * 0.6 + 3^2 * 0.24 + 4^2 * 0.08 = 5.92

Variance = E(X^2) - (E(X))^2

              = 5.92 - (2.32)^2

             = 0.5376

standard deviation = sqrt(0.5376) = 0.7332

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