2. (8 Marks - 2 points each) Suppose you toss a fair coin four times. Let...
4. Toss a fair coin 6 times and let X denote the number of heads that appear. Compute P(X ≤ 4). If the coin has probability p of landing heads, compute P(X ≤ 3) 4. Toss a fair coin 6 times and let X denote the number of heads that appear. Compute P(X 4). If the coin has probability p of landing heads, compute P(X < 3).
2. SUPPLEMENTAL QUESTION 1 (a) Toss a fair coin so that with probability pheads occurs and with probability p tails occurs. Let X be the number of heads and Y be the number of tails. Prove X and Y are dependent (b) Now, toss the same coin n times, where n is a random integer with Poisson distribution: n~Poisson(A) Let X be the random variable counting the number of heads, Y the random variable counting the number of tails. Prove...
You toss a fair coin four times in a row. What is the probability of getting four tails?
A fair coin is tossed 3 times. Let X denote a 0 if the first toss is a head or 1 if the first toss is a zero. Y denotes the number of heads. Find the distribution of X. Of Y. And find the joint distribution of X and Y.
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.
Problem(13) (10 points) An unfair coin is tossed, and it is assumed that the chance of getting a head, H. is (Thus the chance of setting tail, T. is.) Consider a random experiment of throwing the coin 5 times. Let S denote the sample space (a) (2 point) Describe the elements in S. (b) (2 point) Let X be the random variable that corresponds to the number of the heads coming up in the four times of tons. What are...
Extra question: Toss a coin three times. Let X denote the number of heads in the results. Let Y denote the absolute value of the difference between the number of heads and the number of tails. What is the frequency function of (X,Y)?
3. (PMF – 8 points) Consider a sequence of independent trials of fair coin tossing. Let X denote a random variable that indicates the number of coin tosses you tried until you get heads for the first time and let y denote a random variable that indicates the number of coin tosses you tried until you get tails for the first time. For example, X = 1 and Y = 2 if you get heads on the first try and...
A fair coin is tossed n times. Let X be the number of heads in this n toss. Given X = x, we generate a Poisson random variable Y with mean x. Find Var[Y]. Answer depends on n.
A fair coin is tossed four times and let x represent the number of heads which comes out a. Find the probability distribution corresponding to the random variable x b. Find the expectation and variance of the probability distribution of the random variable x