Let X = 1 if a randomly selected vehicle passes an emissions test and X = 0 otherwise. Then X is a Bernoulli rv with pmfp(1) = p and p(0) = 1 - p. (a) Compute E(X²). E(X²) = (b) Show that V(X) = P(1 - p). V(X) = E = = P(1 - p) (c) Compute E(X⁹8). E(X98) = - [E(X)]²

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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
=
= : p(1 - p)
(c) Compute E(X98).
E(X98) =
- [E(X)]²
Transcribed Image Text: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 = = : p(1 - p) (c) Compute E(X98). E(X98) = - [E(X)]²
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