A5 Consider an experiment where you toss a coin as often as necessary to turn up...
Imagine an experiment where we flip a coin 6 times, and get “head, tail, head, head, head, head”. Which of the following statements are true? a) The coin is not fair b) The coin’s tail probability is 1/6 c) The sequence "head, tail, head, head, head, head" is an outcome in the sample space. d) The sample space of the experiment is {head, tail}
Suppose you toss an unfair coin 8 times independently. The probability ofgetting a head is 0.3. Denote the outcome to be 1 if you get a head and 0 if a tail. (i) Write down the sample space Ω. (ii) What is the probability of the event that you get a head or a tail at least once? (iii) If you get eight same toss's you will get x dollars, otherwise you will lose 1 dollar. On average, how large...
You toss a penny and observe whether it lands heads up or tails up. Suppose the penny is fair, i.e., the probability of heads is 1/2 and the probability of tails is y. This means every occurrence of a head must be balanced by a tail in one of the next two or three tosses. if I flip the coin many, many times, the proportion of heads will be approximately %, and this proportion will tend to get closer and...
9.74. Suppose we toss a biased coin independently until we get two heads or two tails in total. The coin produces a head with probability p on any toss. 1. What is the sample space of this experiment? 2. What is the probability function? 3. What is the probability that the experiment stops with two heads?
9. Suppose X and Y are the sum and difference of two coin tosses where = head and 0-tail for each toss. The joint PMF is given by: 0 00.25 0 10.25 0 0.25 2 0 0.25 0 a) Compute cov(X, Y). (b) Are X and Y uncorrelated? (c) Compute P(X = 0), P(Y = 0), and P(X = 0, Y = 0) (d) Are X and Y independent? Answer: 0; Yes; 0.25, 0.5, 0.25; No
Tossing an unfair coin with P(H) = 0.6 and P(T) = 0.4. The coin is tossed 10 times (each toss is independent from others) and in any turn it shows heads, it is tossed again. We want to count the cases where the coin is tossed twice and the second toss, too, is head. For example, H T T T T T T T H T H T In this case, the count will be 1. Only the first turn...
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...
1. Consider the experi We toss a coin until we obtain a head Wrie down the sample space for this experiment. Write down the event: EWe obtain a head within 3 tosses) as a subset of the sample space. 2. We take a rod of length 1 metre and randomly divide it into two pieces. Write down the sample space for this experiment. Can you plot it? Write down the event E that at least one of the pieces has...
The experiment is flipping a fair coin twice Let A be the event the first toss is heads and be the event the second toss is heads." What is PAU , the probability of Apr 07 Hint You will need to use the addition rule of probability. Listing the sample space is one way to figure out PAD). 2.71 points 00 0.50 0.75 0.25
QUESTION 7 Which of the two events are mutually exclusive? OA. Toss a coin to get a head or tail OB. Roll a die to get an even number or 4 OC. Roll two dices to get two even numbers or a sum of 8 D. Roll a die and get a prime number or 3 QUESTION 8 Probability of events must lie in limits of OA. 1-2 B. 2-3 OC.0-1 OD.-1-1 QUESTION9 Sample space (e.g. all possible outcomes) for...