Question

a fair coin is tossed 3 times. A person receives rupees X^2 if he if he gets X number of heads in all find is expected gain?​

Answer 1

Answer:

2.25 rupees

Step-by-step explanation:

when a fair coin is tossed , there are two possibilities

Head ( success) with probability p = 0.5

Tail (failure) with probability (1-p) = 0.5

since there are 3 trials, then  

the number of heads is a random variable with  a Binomial (n=3,p=0.5) distribution

The mean (expected value) of a binomial distribution is;

mean= n*p

therefore the expected number of heads is

n*p= 3*0.5=1.5

If the person receives x^2 rupees for x heads, then the expected gain is

1.5^2=2.25

2.25 rupees