# An unfair coin with Pr[H]=0.1 is flipped 3 times. A random variable X is defined as the number of heads plus twice the number of tails. Find the density function that corresponds to these values of...

An unfair coin with Pr[H]=0.1 is flipped 3 times. A random variable X is defined as the number of heads plus twice the number of tails. Find the density function that corresponds to these values of X:

3, 4, 5, 6

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### 1 Answer

Pr(H)=0.1

Pr(T)=1-0.1=.9

Its sample space is

`S={HHH,HHT,HTH,THH,HT T,THT,T TH ,T T T }`

X 3 4 5 6

wHEN

X =3 {HHH}

Pr(X=3)= `(.1)xx(.1)xx(.1)=1/1000`

X =4 {HHT,HTH,THH}

Pr(X=4)=`3(.1xx.1xx.9)=27/1000`

X = 5 {HTT,THT,TTH}

Pr(X=5)=`3xx(.1xx.9xx.9)=243/1000`

X =6 {TTT}

Pr(X=6)= `.9xx.9xx.9=729/1000`

X 3 4 5 6

Pr(X) 1/1000 27/1000 243/1000 729/1000