3. (PMF – 8 points) Consider a sequence of independent trials of fair coin tossing. Let...
4. Let 210,1,2) be the outcome space in a model for tossing a coin twice and observing the total number of heads. Say if the following events can be represented as subsets of Ω. If you say "yes," provide the subset; if you say "no," explain why: a) the coin does not land heads both times; bon one of the tosses the coin lands heads, and on the other toss it lands tails; Section 1.3. Distributions 31 C) on the...
Q.1 (25') Pony is playing coin tossing game with Yanny. They found the coin have 4 heads and 6 tails in 10 flips. Let p be the probability for obtaining a head, based on the first 10 flips a) Can we conclude it is a biased or fair coin base on the result above? b) Plot the Bernoulli's PMF What is the probability for obtaining 6 heads in 10 flips using the same coin? d) What is the probability for...
5. (15 pts) Let S denote the sample space of tossing the HK dollar coin 9 times with success probability pon the Number side and failure probability g = 1-pon the Flower side. For i=1,2,..., 100, let X, denote the random variable on 2, having value 1 for the outcomes w i th in the number sicle and zero otherwise. Let Y = 3.X1 +3.X2 + ... +3X100- (a)(2 pts) Are the random variables X1,..., X, independent? (b)(3 pts) Find...
Consider the experiment of tossing a fair coin four times. If we let X = the number of times the coin landed on heads then X is a random variable. Find the expected value, variance, and standard deviation for X.
3. Suppose my friend and I are tossing a biased coin (the chance of the coin landing heads is 0.48). I get one dollar each time the coin lands heads, and I have to pay one dollar to my friend each time it lands tails. I will stop playing if my net gain is three dollars. (a)What is the chance that I will stop after exactly three tosses? (b) What is the chance that I will stop after exactly four...
Wiout feplacement. 6.9 Consider a sequence of Bernoulli trials with success probability p. Let X denote the number of trials up to and including the first success and let Y denote the number of trials up to and including the second success. a) Identify the (marginal) PMF of X c) Determine the joint PMF of X and Y. d) Use Proposition 6.2 on page 263 and the result of part (c) to obtain the marginal PMFS of X and Y....
A fair coin is tossed 20 times. Let X be the number of heads thrown in the first 10 tosses, and let Y be the number of heads tossed in the last 10 tosses. Find the conditional probability that X = 6, given that X + Y = 10.
A fair coin is tossed 20 times. Let X be the number of heads thrown in the first 10 tosses, and let Y be the number of heads tossed in the last 10 tosses. Find the conditional probability that X = 6, given that X + Y = 10.
A fair coin is flipped independently until the first Heads is observed. Let the random variable K be the number of tosses until the first Heads is observed plus 1. For example, if we see TTTHTH, then K = 5. For k 1, 2, , K, let Xk be a continuous random variable that is uniform over the interval [0, 5]. The Xk are independent of one another and of the coin flips. LetX = Σ i Xo Find the...
a fair coin is tossed until either a head turns up or 3 tosses are made. let x be no of heads which occur and let y be no of tails. find expected value and variance of x and y