Let X be a standard normal random variable. Find E[2X2 + 1] UESTION 2 Roll two f

Question

Let X be a standard normal random variable. Find E[2X2 + 1] UESTION 2 Roll two fair dice. If we denote random variables E, F, and G as E = { Sum of two numbers is 6), F- { First die shows 4), and G Sum of two numbers is 7) OE and F are independent OE and F are not independent O E and F are mutually exclusive Unable to tell with the given information UESTION 3 Which of the following statements is true? O F and G are independent O F and G are not independent O F and G are mutually exclusive Unable to tell with the given information

Explanation / Answer

As multiple questions are posted, only the first one will be answered.

1. Given, E(X) = 0 and V(X) = 1

V(X) = 1

or, E(X2) - [E(X)]2 = 1

or, E(X2) - 0 = 1

or, E(X2) = 1

E[2X2 + 1] = 2E[X2] + 1 = 2*1 + 1 = 3

Answer: 3

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