Let X be the number of heads in n tosses of a fair coin. For each...
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.
independent. Let Sa be the number of A fair coin is tossed n times. Assume the n trials are lower bound on the probability that heads obtained. Using Chebyshev's inequality, find a differs from 0.5 by less than 0.1 when n = 10,000. How many trials are needed to ensure that this lower bound exceeds 0.999 ?
independent. Let Sa be the number of A fair coin is tossed n times. Assume the n trials are lower bound on the...
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)...
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 biased coin is tossed n times. The probability of heads is p and the probability of tails is q and p=2q. Choose all correct statements. This is an example of a Bernoulli trial n-n-1-1-(k-1) p'q =np(p + q)n-1 = np f n- 150, then EX), the expected value of X, is 100 where X is the number of heads in n coin tosses. f the function X is defined to be the number of heads in n coin tosses,...
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...
1. A fair coin is flipped until three heads are observed in a row. Let denote the number of trials in this experiment. [This is a simple model of some procedures in acceptance control]. b) Find p(x) for the first five values of X c) Make an estimate of EX. Hint: use geometric rv related to X.
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).
Let X be the random number of fair coin tosses till the third head appears. For example, if the outcomes are h, t, h, t, h, then X-б. Find E(X).