Suppose you are conducting a hypothesis test to compare two sample means from independent samples, with the variance unknown, but you know it is the same for both populations. Then you use the pooled estimate of the variance given by [ (n1 - 1)s1^2 + (n2-1)s2^2 ] / (n1+n2-2)
I was just...
what about if you had f(x,y) = x^2+y^2 again, but with y a function of x. The for the partial derivative of f with respect to x, you keep y fixed (?) and let x vary, even though y is a function of x (?). Thanks.
thats what i was confused about. we treat the x and y as independent variables, even though they won't really vary independently (since both depend on t)
if you are given f(x,y)=x^2+y^2 and y=cos(t) x=sin(t), then when you differentiate f with respect to t, you use the partial derivatives of f with respect to x and y in the process. When i was taught partial derivatives, i was told that we "keep all but one of the independent variables fixed..."...
if we know that an infinite series is convergent from an integer T, to infinity, then the series is convergent from 1 to infinity. conversely, if a series is convergent from 1 to infinity then it is convergent from T to infinity (i.e. starting point of the series does not affect...
hey, i was just wondering if anyone could help find the sum of the infinite series defined by 1/[n(n+1)(n+2)]. I can split it into partial fractions but not sure from there. Thanks
does anyone know a proof for the solution to the frobenius problem for n=2? that is, that the smallest not possible number expressable as a linear combination of a and b is (a-1)(b-1)??
this is quite a classic problem i think but I am having difficulty finishing it off. If we have two stamps of positive values a and b, (greater than 1), what values can be expressed as a linear combination of these 2 stamps. If the stamps have a highest common factor greater than 1, then there...