Can anyone please help me with this advance statistics problems ?

Question

I have put the questions on the following website; http://www.mbi-fasteners.com/stat.gif

Answer 1

I noticed you posted the first part of this question as another question on answers so I'll work on that and answer that one there. for the question 2,

The Oxford Dictionary of Statistical Terms
Yule - Simpson paradox: The effect whereby a contingency table may show a positive dependence between two classification factors at each level of a third factor, but a negative dependence between them when merged over the levels of the third factor.

Elementary Probability by David Stirzaker
Two drugs are being tested. Of 200 patients given drug A, 60 are cured; and of 1100 given drug B, 170 are cured. If we assume a homogeneous group of patients, find the probabilities of successful treatment with A or B. Now closer investigation revels that the 200 patients given drug A were in face 100 men, of whom 50 were cured, and 100 women of whom 10 were cured. Further of the 1100 given drug B, 100 were men of whom 60 were cured, and 1000 were women of whom 110 were cured. Calculate the probability of cure for men and women receiving each drug; note that B now seems better than A. (results of this kind indicate how much care is needed in design of experiments. Note that the paradox was described by Yule in 1903, and is also called the Yule - Simpson paradox.)

here you have P(A) = 60%, P(B) = 15.45%, looks like drug A is better

P(A | male) = 50%
P(B | male) = 60%
so for males it looks like B is better

P(A | female) = 10%
P(B | female) = 11%
so for females B is better.

what a paradox!

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for the MLE of the Poisson, Let L be the likelihood function.

L = ∏ λ ^ x exp(-λ) / x!
= λ ^ (∑x) * exp( - 6λ) / ∏x!

ln L = - 6λ + ∑x * ln(λ) - ln∏x!

take the partial derivate of ln L wrt λ to get:

∂ lnL / ∂ λ = -6 + ∑x / λ

set equal to zero and solve for λ. You'll find that λ = ∑x / 6, the mean of the samples. this is Maximum Likelihood Estimator for λ.


in excel list the values know in columns A B C D E and then the values 0, 1, 2, 3, in column 4.

plot the above equations and you'll be set.

Answer 2

to be certain that the function to be a risk density function, a pdf, the vital over the desired era could equate to a million. one thousand ?(2x) * ((one thousand-x)^2) / (10^12) dx = a million/6 0 that's not a risk mass function if I easily have omit study the equation then in step with risk that's a density function. all you may desire to do is teach that's going to combine to a million. for the different area of the concern, in case you have a pdf f(x) you may desire to unravel for x x ?f(t) dt = 0.ninety 5 0