I only need help with 7 a and 8 Thanks The best constant tha

I only need help with 7 (a) and 8. Thanks.

The \"best\" constant that approximates a random variable. Let X be a random variable. What is the constant b that minimizes E[(X - b)2]? Ex. 2.8 in Section 2.2. St. Petersburg paradox Consider the following game: you flip a fair coin until you observe a Tail and let X be the number of tosses. If X = 1, you win $1, if X = 2, you win $2, if X = 3, you win $4, if X = 4, you win $8, if X = 5, you win $16 etc. What is the expected value of your profit?

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