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A processor of carrots cuts the green top off each carrot, washes the carrots, and inserts six into a package. Twenty packages are inserted in a box of shipment. To test the weight of the boxes, a few were checked. The mean weight was 20.4 pounds, the standard deviation 0.5 pounds. How many boxes must the processor sample to be 95% confident that the sample mean does not differ from the population mean by more than 0.2 pounds? 95% = .95-1 =...

Quote: Originally Posted by bbrown79 a. binomial distribution right? I think i just misread the question on a. c. on wikipedia is says standard deviation = (p(1 − p)/n). so it would be (.3(1-.3)/12) = .0175 is this right? a. yes, it's a binomial distribution c. the formula you found is the variance formula. take a square root

For (a) I got to f(y1,y2) = y1 + y2 E(y1) = ∫(0)->(1)∫(0)->(1) y1*f(y1,y2) dy1 dy2 = ∫(0)->(1)∫(0)->(1) y1(y1 + y2) dy1 dy2 = ∫(0)->(1)∫(0)->(1) y1^2 + y1y2 dy1 dy2 Then Im not really sure how to integrate y1 from y1^2 + y1y2. How do you integrate this?

OK, to solve for (a) you need to find your marginal densities. For the sake of typing and for clarity, let me rewrite the problem with easier variables: let Y1 = X let Y2 = Y You don't have to do this, but I find it easier to follow because I'm used to the xy-plane. Your joint density is f(x, y) = X + Y, in the region 0 < x < 1, 0 < y < 1. The marginal density of X, fx(x) = ∫x + y dy, integrate...

Quote: Originally Posted by kingwinner Let X_n be a sequence of independent random variables such that P(X_n=0)=1-1/n and P(X_n=1)=1/n Then X_n converges in probability to 0. By Borel-Cantelli's lemma, since ∞ ∑ 1/n = ∞ (diverges), n=1 X_n does NOT converge almost surely to 0. Borel Cantelli Lemma: Let A1,A2,A3,... be events. (i) if ∑P(An)<∞, then P(An io)=0 (ii) if the A's...

It's the last question in my assignment. I have already worked out that the sensitivity and specificity of a test go in opposite directions depending on how you adjust your cut-off value. However, the question afterwards asks "Discuss the implications of these findings for the development of new tests." Thanks to anyone who can help. EDIT: sentificity!?? What the hell lol. I meant *specificity.

Quote: Originally Posted by Martingale since P(X_n=1)=1/n by the B-C Lemma we know that [X_n=1 i.o.] if this is the case how could X_n converge almost surely to zero? By part (ii) of B-C lemma, since ∑ P(X_n=1)= ∑1/n = ∞, this implies that P(X_n=1 io)=1, but WHY does this imply that Xn does not converge almost surely to 0? I don't understand this. Does it converge almost surely to any other value? If it does...

Hi, Can any body help with the following problem: a medical practitioner is interested in measuring the success of a drug on n = 100 patients. Let Xi be the Bernoulli random variable, with Xi = 1 denoting success and Xi = 0 denoting failure. Let Y = sum of Xi ,denote the total number of successes. Assume that the success probability is constant across patients and is a random variable p which follows a Beta(10, 2) distribution 1) Obtain the...

Hey guys, great forum! I've got a problem: I own 3 tools, which have average time of life 4, 6 and 8 days (exponential distribution). How can I find the probability that these tools are working after 2 days?

use the distribution function and remember that the exponential distribution of these 3 tools is equivalent to an exponontial distribution with mean 18. .i.e 1/lambda = 18