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...
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.
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?
A fair coin is tossed five times. Let X denote the number of heads. Find the variance of X.
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.
A, B, and C please Toss a fair coin 11 times. Let X be the number of heads. (a) Find P(X= 7). (b) Find P(X29). (c) Find P(X 58). (a) P(X = 7) = (Round to four decimal places as needed.)
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 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.
We toss a fair coin n 400 times and denote Zn the number of heads. (a) What are E(Zn) et Var(Zn)1? (b) What is the probability that Z 200? (use the normal approximation together with the continuity correction (c) What is the smallest integer m such that Pr 200-mくZ.く200 +m] > 20%? (use the normal approximation together with the continuity correction). We toss a fair coin n 400 times and denote Zn the number of heads. (a) What are E(Zn)...