a) The sample space S will be consisting of
S={HH,HT,TH,TT}
2. Consider tossing a coin twice. Denote H ="head" and T ="tail" (a) List all outcomes...
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...
Example: A coin is tossed twice. Let X denote the number of head on the first toss and Y denote the total number of heads on the 2tosses. Construct the join probability mass function of X and Y is given below and answer the following questions. f(x, y) x Row Total 0 1 y 0 1 2 Column Total (a) Find P(X = 0,Y <= 1) (b) Find P(X + Y = 2) (c) Find P(Y ≤ 1) (d)...
4 PROBABILITY (16) An experiment consists of tossing a fair coin (head and tail T) three times. The sample space S in this experiment is S - (HT), and a possible event Ecould be E = {H,H). (1) True. (2) False (17) Which of the following statements is true? (1) The set of all possible events of an experiment is called the sample space, S. (2) If an experiment is performed more than once, one and only one event can...
An experiment consists of tossing a fair coin (head H, and tail T) three times. The sample space S in this experiment is S = {H, T}, and a possible event E could be E = {H,H}. (1) True. (2) False.
Flip a coin twice and observe its face side. Assume that the coin is unfair with P(head)=0.6. Define the following events: •A: you get at least one head •B: you get at least one tail Write out sample space S, events A,B by listing all possible outcomes. (b) FindP(A), P(B) (c) FindP(A∪B),P(A∩B) (d) FindP(A|B) (e) Are A,B independent? and why?
part C (b) Consider the experiment on pp. 149-156 of the online notes tossing a coin three times). Consider the following discrete random variable: Y = 2[number of H-3[number of T). (For example, Y (HHT) = 2.2-3.1=1, while Y (TTH) = 2.1-3.2 = -4.) Repeat the analysis found on pp. 149-156. That is, (i) find the range of values of Y: (ii) find the value of Y(s) for each s ES: (iii) find the outcomes in the events A -Y...
a. List all possible outcomes in the sample space.b. Find the probability associated with each outcome.c. Let A be the event “exactly 2 heads.” Find P ( A ).d. Let B be the event “at most 1 head.” Find P ( B ).e. Let C be the event “at least 2 heads.” Find P ( C ).f. Are the events A and B mutually exclusive? FindP ( A or B ).g. Are the events A and C mutually exclusive? FindP...
A biased coin has a 40% chance of producing a head. If it is tossed 10 times, What is the probability of getting exactly 3 heads? b. a. What is the probability of getting 3 or more heads. (This can be calculated in two different ways. The easier way uses the complement rule.) a. Find the value of C for which the function f(x) probability density function. b. Use your density function in (a) to find PCO s X 1)...
A box contains five coins. For each coin there is a different probability that a head will be obtained when the coin is tossed. (Some of the coins are not fair coins!) Let pi denote the probability of a head when the i th coin is tossed (i = 1, . . . , 5), and suppose that p1 = 0, p2 =1/4, p3 =1/2, p4 =3/4, p5 =1. The experiment we are interested in consists in selecting at random...
1. Consider flipping a fair coin three times and observe whether it lands heads up or tails up. Let X the number of switches from either head to tail or vice versa. For example, when THT is observed, the number of switches is 2 and when HHH is observed, the number of switches is 0. Also, let Y be the number of tails shown in the three times of fipping. (a) List all the values of the joint probability mass...