# 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

aruv | High School Teacher | (Level 2) Valedictorian

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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