Question

QUESTION 8 Problem 8) A fair coin is tossed 20 times. A fair coin means that the probability of getting a head is the same as the probability of getting a tail. Let X be the number of coins of getting head. Note that there are only two possible outcomes: getting head or tail after tossing the coin. X follows a binomial distribution with n=20, p=0.5. Answer the following questions. (Question) Find the expected value of X, E(X). QUESTION 9 Problem 9) A fair coin is tossed 20 times. A four coin means that the probability of getting a head is the same as the probability of getting a tail. Let X be the number of coins of getting head Note that there are only two possible outcomes getting head or tail after tossing the coin X follows a binomial distribution with a - 20.0-0.5. Answer the following questions (Question) Find the variance of X Varcx).

Answer 1

Let n be no. of trails ,p be the probability

Formula for expected value E(X) in binomial distribution is= n*p

Formula for variance Var(X) in binomial distribution is = n*p*(1-p)

8)

Given that

n=20

P=0.5

Expected value E(X)= n*p=20*0.5= 10

E(X)=10

9)

Given that

n=20

P=0.5

1-p= 0.5

Var(X)= n*p*(1-p)=20*0.5*0.5=5

Var(X)= 5