Question: Problem 1. [4 marks] Let Z N N(0,1) and (13(2) be its CDF. Let X m N0], = 3,02 = 9). (1a) [1 mark] It

Problem 1. [4 marks] Let Z N N(0,1) and (13(2) be

Problem 1. [4 marks] Let Z N N(0,1) and (13(2) be its CDF. Let X m N0], = 3,02 = 9). (1a) [1 mark] It is known that (M196) 2 0.975. Find 55* such that P(X g 29*) = 0.025. (1b) [2 marks] Let U 2 3X + 1. Show that U has a normal distribution by deriving its MGF. (10) [1 mark] Consider a transformed variable Y = 1+2X . Find its expected value E (Y)

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5. It is the needs of the individual that are important.

6. It is what the person has previously done for the group that is the deciding factor.

3. It is the commitment you show that is the deciding factor.