(Question Consider a biased coin where P(Head) = p = 1-q, i.e. it is Bern(p) This...
A biased coin is tossed n times. The probability of heads is p and the probability of tails is q and p=2q. Choose all correct statements. This is an example of a Bernoulli trial n-n-1-1-(k-1) p'q =np(p + q)n-1 = np f n- 150, then EX), the expected value of X, is 100 where X is the number of heads in n coin tosses. f the function X is defined to be the number of heads in n coin tosses,...
A biased coin is tossed until a head occurs. If the probability of heads on any given toss is .4, What is the probability that it will take 7 tosses until the first head occurs? The answer i got was , (.60)^2(.40) Now for the second part it says, what is the probability that it will take 9 tosses until the second head occurs. Is the answer for this part be 9C2(.40)^2(.60)^7 or 8C1(.40)(.60)^5 I can't figure out if its...
Consider a coin with probability q of landing on heads, and probability 1−q of landing on tails. a) The coin is tossed N times. What is the probability that the coin lands k times on heads. b) The coin is tossed 100 times, and lands on heads 70 times. What is the maximum likelihood estimate for q?
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
A biased coin with probability 0.6 to land on head is flipped 6 times, calculate the probability of: - exactly two heads, - at most one tail, - even number of heads.
You have a biased coin, where the probability of flipping a heads is 70%. You flip once, and the coin comes up tails. What is the expected number of flips from that point (so counting that as flip #0) until the number of heads flipped in total equals the number of tails?
1. Let p-: P(head) when a coin is tossed, and consider the hypotheses Ho : p-0.5 and H. : p-0.1. Suppose the coin is tossed 10 times, and te critcal region is defined by "get 2 heads or less". That is the null hypothesis is rejected if the number of observed heads is 2 or less. (a) Find the significance level of the test (a). (b) Find the power of the test (1 -B).
Problem 4. A fair coin is tossed consecutively 3 times. Find the conditional probability P(A | B), where the events A and B are defined as A-(more heads than tails came upl, B-(1st toss is a head) 1St toss is a head Problem 5. Consider rolling a pair of dice once. What is the probability of getting 7, given that the sum of the faces is an odd number?
E. A coin with probabiltiy p of heads is tossed till the first head occurs. It 1S is then tossed again till the first tail occurs. Let X be the total number of tosses required (a) Find the PMF of X, (b) Find the mean and variance of X
Suppose we toss a coin (with P(H) p and P(T) 1-p-q) infinitely many times. Let Yi be the waiting time for the first head so (i-n)- (the first head occurs on the n-th toss) and Xn be the number of heads after n-tosses so (X·= k)-(there are k heads after n tosses of the coin). (a) Compute the P(Y> n) (b) Prove using the formula P(AnB) P(B) (c) What is the physical meaning of the formula you just proved? Suppose...