Question

Let X = 1 if a randomly selected vehicle passes an emissions test and X = 0 otherwise. Then X is a Bernoulli rv with pmf p(1) = p and p(0) = 1 - p. (a) Compute E(X²). E(X²) = (b) Show that V(X) = p(1 - p). V(X) = E( ) - [E(X)]² = - p² = p(1 - p) (c) Compute E(X??). E(X??) =

          Let X = 1 if a randomly selected vehicle passes an emissions test and X = 0 otherwise. Then X is a Bernoulli rv with pmf p(1) = p and p(0) = 1 - p.
(a) Compute E(X²).
E(X²) = 
(b) Show that V(X) = p(1 - p).
V(X) = E( ) - [E(X)]²
= - p²
= p(1 - p)
(c) Compute E(X??).
E(X??) =

Let X = 1 if a randomly selected vehicle passes an emissions test and X = 0 otherwise. Then X is a Bernoulli rv with pmf p(1) = p and p(0) = 1 - p.
(a) Compute E(X²).
E(X²) =
(b) Show that V(X) = p(1 - p).
V(X) = E( ) - [E(X)]²
= - p²
= p(1 - p)
(c) Compute E(X??).
E(X??) =

Added by Michael G.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Krishna G

03/22/2022

Step 1

Step 1: Compute E(X^2) Given that X is a Bernoulli random variable with pmf p(1) = p and p(0) = 1 - p, we have: E(X^2) = (1^2)*p + (0^2)*(1 - p) E(X^2) = p Show more…

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Let X = 1 if a randomly selected vehicle passes an emissions test and X = 0 otherwise. Then X is a Bernoulli rv with pmf p(1) = p and p(0) = 1 - p. (a) Compute E(X²). E(X²) = (b) Show that V(X) = p(1 - p). V(X) = E( ) - [E(X)]² = - p² = p(1 - p) (c) Compute E(X⁸⁷). E(X⁸⁷) =