Value of c makes f a valid pdf


Consider a continuous random variable X with the following pdf: f(x) = ( (1/2)x + (1/4) for 1 <= x <=c, 0 otherwise, where c is an unknown constant.

(a) What value of c makes f a valid pdf? (use this value c for remaining questions)

(b) What is E[X]?

(c) What is Var(X)? (Hint: first think about which variance formula is easiest to apply.)

(d) What is E[4X- 1]?

(e) What is Var(4X - 1)?

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Basic Statistics: Value of c makes f a valid pdf
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