examples how to estimate fraction
Best Results From Yahoo Answers Youtube
From Yahoo Answers
Answers:Not easy to find something about Estimate fractions------------------------------------------------ Estimate With Fractions http://www.boiseschools.org/schools/trailwind/classrooms/room15/Math%20PDF/Chapter%2010/5HMM-RE-10-01.pdf --------------------------http://www.boiseschools.org/schools/trailwind/classrooms/room15/Math%20PDF/Chapter%2010/5HMM-HW-10-01.pdf------------------Estimate fractions http://www.lessonplanet.com/search?keywords=estimate+fractions&rating=3------------- Estimating with Fractions http://go.hrw.com/resources/go_mt/hm2/so/c2ch3bso.pdf Fraction Cafe http://www.factmonster.com/math/knowledgebox/fractioncafe.html http://mathforum.org/paths/fractions/edible.fractions.html
Answers:Yes, you're correct, theta_hat is a random variable and when you compute the expectation E(theta_hat) you will use a probability distribution with an unknown parameter theta. In general bias(theta) = E(theta_hat) - theta is then a function of this parameter theta, it could happen that this is a constant function (doesn't vary with theta). In your binomial example, you didn't say what estimator for p that you want to use, but I guess it is p_hat = Y/8. f_p_hat(x) means the probability distribution for the random variable p_hat. In this example p_hat could take the values 0/8, 1/8, 2/8, ..., 8/8. The probability that p_hat is k/8 is the same as the probability that Y=k, this means the probability that you get k successes in the 8 trials. This probability is f_p_hat(k/8) = C(8,k)*p^k*(1-p)^(8-k) for k=0,1,...,8 and f_p_hat(x) = 0 for all other values of x. (C(n,k) = n!/(k!*(n-k)!) is the binomial coefficient) Now that you have f_p_hat(x) you can compute E(p_hat) E(p_hat) = sum f_p_hat(k/8)*k/8 The sum (and all sums in the sequel) goes from k=0,1,...,8. So you get E(p_hat) = sum C(8,k)*p^k*(1-p)^(8-k)*k/8 Now consider the function f(a,b) = sum C(8,k)*a^k*b^(8-k) = (a+b)^8 and differentiate it with respect to a to get df(a,b)/da = sum C(8,k)*k*a^(k-1)*b^(8-k) and you see that E(p_hat) = p/8*df(p,1-p)/da This means you differentiate first, then evaluate the derivative in the point (a,b) = (p, 1-p). Now to evaluate this function we can use the other expression for f(a,b) and differentiate that to get df(a,b)/da = 8*(a+b)^7 Substituting a=p, b=1-p gives us df(p,1-p)/da = 8 So finally E(p_hat) = p/8 * 8 = p Thus bias(p_hat) = p - p = 0 and this is an unbiased estimator. The function turned out to not depend on p and more than that, it is 0 (which means the estimator is unbiased).
Answers:Blood is a fluid tissue.
Answers:Dilutions are calculated like this: m1v1=m2v2 where m is g or mol/L and v is volume. So you want to find m1, plug in everything else, amount diluted in L or mL=v1, amount you found is m2, and total volume after dilution is v2. This is a very handy formula, I highly recommend you commit it to memory.