A coin will be tossed multiple times. Probability of
head is 1/2, and probability of tail is 1/2. they are independent
from each other.
X is a random variable that counts how often the coin must be
tossed until the first head appears.
calculate for all k=1,2,3,..., how big the probability is
for:
i) X=k
ii) X>k
iii) X<k
A coin will be tossed multiple times. Probability of head is 1/2, and probability of tail is 1/2....
A coin is tossed 100 times, each resulting in a tail (T) or a head (H). If a coin results in a head, Roy have to pay Slim 500$. If the coin results in a tail, Slim have to pay Roy 500$. What is the probability that Slim comes out ahead more than $20,000?
A coin with probability p is tossed until the first head occurs. It is then tossed again until the first tail occurs. Let X be the total number of tosses required. 1) Find the distribution function of X. 2) Find the mean and variance of X.
A coin is tossed and has three possible outcomes: Head, Tail, Edge. Suppose P(Head) = 1/3, P(T ail) = 1/2, P(Edge) = 1/6. The coin is repeatedly tossed. If the trials are identical and independent, what is the probability of getting a head before getting a tail?
A coin with probability p of heads is tossed until the first head occurs. It is then tossed again until the first tail occurs. Let X be the total number of tosses required. (i) Find the distribution function of X. (ii) Find the mean and variance of X
Problem 7) True/False 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. True/False: In this problem, the random variable X is considered as a...
Problem 10) 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 tril. 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 PX-17).
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...
A fair coin is tossed 10 times. What is the probability that the coin lands head at least 8 times? a) 0.0527 b) 0.0547 c) 0.1094 d) 0.0440 e) 0.0537
1. There is this coin that is not balanced. The probability of getting a head is four times the probability of getting a tail. Suppose this coin is tossed 5 times. Give the probability of getting at least 1 head. Express your answer as a decimal to several places past the decimal or as a common fraction. Show work.
question: A fair coin is tossed 3 times. Show that the events “at least one head & at least one tail” and “heads on the 2nd toss” are independent