3. Let X be a continuous random variable. Let f(x) = c(x − 1)³ and Sx = [1,3]. Hint: (x - 1)³ = x³ + 3x − 3x² - 1 (a) What value of c will make f(x) a valid density? (b) What is P(X = 2)? (c) Find E(X). (d) What is P(1 < X < 2)?

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3. Let X be a continuous random variable. Let f(x) = c(x − 1)³ and Sx = [1,3].
Hint: (x - 1)³ = x³ + 3x − 3x² - 1
(a) What value of c will make f(x) a valid density?
(b) What is P(X = 2)?
(c) Find E(X).
(d) What is P(1 < X < 2)?
Transcribed Image Text:3. Let X be a continuous random variable. Let f(x) = c(x − 1)³ and Sx = [1,3]. Hint: (x - 1)³ = x³ + 3x − 3x² - 1 (a) What value of c will make f(x) a valid density? (b) What is P(X = 2)? (c) Find E(X). (d) What is P(1 < X < 2)?
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