Toss a fair coin 4 times. Let Y be the number of heads.
(a) What is the probability mass function of Y ? Compare your answer to the probability mass function of Binomial distribution.
(b) What is the cumulative distribution function of Y ?
(c) What is the expected value of Y ?
(d) What is the variance of Y?
Toss a fair coin 4 times. Let Y be the number of heads. (a) What is...
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. Let X be the number of Heads when we toss a coin 3 times. Find the probability distribution (that is, the probability function) for X.
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)?
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.
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
Suppose a fair coin is tossed 280 times. Find the probability that the number of Heads observed is 151 or more. Use Binomial Distribution and Normal Approximation and compare the results.
Problem 7. Suppose that a coin will be tossed repeatedly 100 times; let N be the number of Heads obtained from 100 fips of this coin. But you are not certain that the coin is a fair coin.it might be somewhat biased. That is, the probability of Heads from a single toss might not be 1/2. You decide, based on prior data, to model your uncertainty about the probability of Heads by making this probability into random variable as wl....
A fair coin is tossed 10 times and the number of heads is counted. Complete parts (a) through (d). a. Use the binomial distribution to find the probability of getting 5 heads. (Round to four decimal places as needed.) b. Use the binomial distribution to find the probability of getting at least 5 heads. (Round to four decimal places as needed.) c. Use the binomial distribution to find the probability of getting 5 to 7 heads. (Round to four decimal...
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...