independent. Let Sa be the number of A fair coin is tossed n times. Assume the...
Use Chebyshev's Inequality to get a lower bound for the number of times a fair coin must be tossed in order for the probability to be at least 0.90 that the ratio of the observed number of heads to the total number of tosses be between 0.4 and 0.6. Let X be a random variable with μ=10 and σ=4. A sample of size 100 is taken from this population. Find the probability that the sum of these 100 observations is less...
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.
Suppose that a coin is tossed three times. We assume that a coin is fair, so that the heads and tails are equally likely. Probability that two heads are obtained in three tosses given that at least one head is obtained in three tosses is ___________ Probability that that one head is obtained in three tosses given that at most one head is obtained in three tosses is ____________ at least one means one or more, at most one means...
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.
If a fair coin is tossed n times, show that the probability of getting at least k heads is
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
A fair coin is tossed five times. Let X denote the number of heads. Find the variance of X.
A fair coin is tossed three times. Let X be the number of heads that come up. Find the probability distribution of X X 0 1 2 3 P(X) 1/8 3/8 3/8 1/8 Find the probability of at least one head Find the standard deviation σx
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....