Question

Draw the distribution of a random variable X, where X is the number of heads in a sequence of 10 flips of a weighted coin that prefers heads twice as much as tails

Answer 1

Let p =probability of head in a single flip

then , 1-p = probability of tail in a single flip

Given , p = 2(1-p)

Let X be the number of heads in a sequence of 10 flips

Then X follow Binomial distribution with n= 10 , p =2/3

Probability mass function of X  is

, x= 0,1,2...10

Probability distribution of number of heads

x	P(X=0)
0	0.000017
1	0.000339
2	0.003048
3	0.016258
4	0.056902
5	0.136565
6	0.227608
7	0.260123
8	0.195092
9	0.086708
10	0.017342

The graph of probability distribution is given below