Question 912044: A loaded coin is tossed 5 times , find the
probability distribution for the number of
heads, if heads are thrice likely to occur than tails.let x be the number of heads that will turn up.Find the mean and variance.
Answer by Edwin McCravy(20064)   (Show Source):
You can put this solution on YOUR website!
P(H)+P(T)=1
P(H)=3P(T)
3P(T)+P(T)=1
4P(T)=1
P(T)=1/4
P(H)=3P(T)
P(H)+3(1/4)=3/4
This is a binomial distribution:
Let x be the number of heads:
x P(x)
0 C(5,0)(3/4)^0(1/4)^5 = 1*3^0/4^5 = 1*1/1024 = 1/1024
1 C(5,1)(3/4)^1(1/4)^4 = 5*3^1/4^5 = 5*3/1024 = 15/1024
2 C(5,2)(3/4)^2(1/4)^3 = 10*3^2/4^5 = 10*9/1024 = 90/1024
3 C(5,3)(3/4)^3(1/4)^2 = 10*3^3/4^5 = 10*27/1024 = 270/1024
4 C(5,4)(3/4)^4(1/4)^1 = 5*3^4/4^5 = 5*81/1024 = 405/1024
5 C(5,5)(3/4)^5(1/4)^0 = 1*3^5/4^5 = 1*243/1024 = 243/1024
mean = n*p = 5*(3/4) = 15/4 = 3.75
variance = n*p*(1-p) = 5*(1/4)(3/4) = 15/16 = 0.9375
Edwin
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