Question

A. Let X be a random variable supported on [0, 1] with PDF f(x) = cx for x ? [0, 1] (1) c is equal to (a) 1 (b) 2 (c) 3 (d) 4 (2) The value of F(1/2) is (a) 0.25 (b) 0.5 (c) 0.67 (d) 0.75 (3) ?(3X + 1) is (a) 1 (b) 2 (c) 3 (d) 4 (4) Var(4 - X) is (a) 1/18 (correct) (b) 1/9 (c) 1/2 (d) 8/18 (5) Let Y = max{X, 1 - X}. The CDF of Y is (Hint: Y ? (1/2, 1)) (a) 2 - 2y (b) 2y (c) 2 (d) 2y - 1 (6) ?(Y) is (a) 1/2 (b) 2/3 (c) 3/4 (d) 1

          A. Let X be a random variable supported on [0, 1] with PDF
f(x) = cx for x ? [0, 1]
(1) c is equal to
(a) 1 (b) 2 (c) 3 (d) 4
(2) The value of F(1/2) is
(a) 0.25 (b) 0.5 (c) 0.67 (d) 0.75
(3) ?(3X + 1) is
(a) 1 (b) 2 (c) 3 (d) 4
(4) Var(4 - X) is
(a) 1/18 (correct) (b) 1/9 (c) 1/2 (d) 8/18
(5) Let Y = max{X, 1 - X}. The CDF of Y is (Hint: Y ? (1/2, 1))
(a) 2 - 2y (b) 2y (c) 2 (d) 2y - 1
(6) ?(Y) is
(a) 1/2 (b) 2/3 (c) 3/4 (d) 1

A. Let X be a random variable supported on [0, 1] with PDF
f(x) = cx for x ? [0, 1]
(1) c is equal to
(a) 1 (b) 2 (c) 3 (d) 4
(2) The value of F(1/2) is
(a) 0.25 (b) 0.5 (c) 0.67 (d) 0.75
(3) ?(3X + 1) is
(a) 1 (b) 2 (c) 3 (d) 4
(4) Var(4 - X) is
(a) 1/18 (correct) (b) 1/9 (c) 1/2 (d) 8/18
(5) Let Y = maxX, 1 - X. The CDF of Y is (Hint: Y ? (1/2, 1))
(a) 2 - 2y (b) 2y (c) 2 (d) 2y - 1
(6) ?(Y) is
(a) 1/2 (b) 2/3 (c) 3/4 (d) 1

Added by Melissa M.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Sanchit Jain

Step 1

- Integrate \( f(x) \) from 0 to 1: \[ \int_0^1 cx \, dx = \left[ \frac{cx^2}{2} \right]_0^1 = \frac{c}{2} \] - Set this equal to 1 and solve for \( c \): \[ \frac{c}{2} = 1 \implies c = 2 \] - Therefore, \( c \) is equal to \( \boxed{b} \). Show more…

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Let X be a random variable supported on [0, 1] with PDF f(x) = cx for x ∈ [0, 1] (1) c is equal to (a) 1 (b) 2 (c) 3 (d) 4 (2) The value of F(1/2) is (a) 0.25 (b) 0.5 (c) 0.67 (d) 0.75 (3) E(3X + 1) is (a) 1 (b) 2 (c) 3 (d) 4 (4) Var(4 - X) is (a) 1/18 (correct) (b) 1/9 (c) 1/2 (d) 8/18 (5) Let Y = max{X, 1 - X}. The CDF of Y is (Hint: Y ∈ (1/2, 1)) (a) 2 - 2y (b) 2y (c) 2 (d) 2y - 1 (6) E(Y) is (a) 1/2 (b) 2/3 (c) 3/4 (d) 1