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(X^2). E(X^2) = (b) Show that V(X) = p(1 - p). V(X) = E( ) - [E(X)]^2 = - p^2 = p(1 - p) (c) Compute E(X^85). E(X^85) =

          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(X^2).
E(X^2) = 

(b) Show that V(X) = p(1 - p).
V(X) = E( ) - [E(X)]^2
= - p^2
= p(1 - p)

(c) Compute E(X^85).
E(X^85) =

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(X^2).
E(X^2) =

(b) Show that V(X) = p(1 - p).
V(X) = E( ) - [E(X)]^2
= - p^2
= p(1 - p)

(c) Compute E(X^85).
E(X^85) =

Added by Manuel S.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Adi S

06/19/2023

Step 1

- We have a Bernoulli random variable \( X \) with \( p(1) = p \) and \( p(0) = 1 - p \). Show more…

Show all steps

Thanks for your feedback!

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(X^2). E(X^2) = (b) Show that V(X) = p(1 - p). V(X) = E( ) - [E(X)]^2 = - p^2 = p(1 - p) (c) Compute E(X^85). E(X^85) =