Question

Toss a coin three times or toss three coins simultaneously, and record the number of heads. Repeat the binomial experi- ment 100 times and compare your relative frequency distribution with the theoretical probability distribution.

Answer 1

See, if we denote X as the total number of heads obtained, then X may take values 0,1,2,3. Now, probability of a toss of a single coin giving head is 1/2. So,

I have used the following R code to compare the relative frequency distribution with the original one. If you run this code, you should get the answer

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x=rbinom(100,3,prob=1/2)

d=data.frame(table(x))

d$Freq=d$Freq/100

d1=data.frame(d,"Theo"=dbinom(0:3,3,1/2))

d1

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You will be able to see that the relative frequency distribution is almost same with the actual probability Distribution.

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