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Distribution of a linear transformation of a discrete random variable

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A discrete model assigns an integer payoff to each outcome

Let \(X\) be the discrete random variable with the following distribution

Define \(Y\) by the rule

Y = 2\,X + 1.

(a)4 marks

Complete the table for the distribution of \(Y\)

Transformed value for row 1 Transformed value for row 3 Transformed value for row 4 Probability for transformed row 1

(b)1 mark

Which formula gives the expected value of \(Y\) from the corresponding quantity for \(X\)?

E(Y)=aE(X)+b

E(Y)=aE(X)-b

E(Y)=aE(X)+ab

Calculate \(E(Y)\)

Expected value of Y