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). EX?) = P (b) Show that V(X) = p(1 - p). V(X) = )- (E(X)? = P -p? = p(1 - p) (c) Compute E(X4). E(X®4) =

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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.
%3D
(a) Compute E(X?).
E(X?) = P
(b) Show that V(X) = p(1 - p).
V(X) = Ex
)- [E(X)]?
= p(1 - p)
(c) Compute E(X84).
E(X4) = P
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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. %3D (a) Compute E(X?). E(X?) = P (b) Show that V(X) = p(1 - p). V(X) = Ex )- [E(X)]? = p(1 - p) (c) Compute E(X84). E(X4) = P Need Help? Read It 3:31 PM ENG 令中 2/27/2022 DELL Esc E1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 F12 PrtScr Insert Delete of # %24 & 1 2 3 4 5 6 Backspace 8 9 %3D Tab E R Y P Caps Lock A D G K L Enter Shift V B N M ? Shift Ctrl Fn Alt t PgUp Alt Ctrl 目 + Home PgDn End Inspiron 14 5000 2-in-1 14EMOR Touen Drnght ene otie huwm Aesve Pen MalliJurmemen OHE CRETA N
Expert Solution
Step 1

Solution:

Let X be the bernoulli random variable having probability mass function is given by 

P(X=x)=px(1-p)1-x     x=0,1

that is  P(1)= p and P(0)= 1-p

 

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