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    B An elementary confusion on discrete or continuous variable

    The question is simply posed as " identity the variables as discrete or continuous. 1) Mark of a student in an examination. 2) Family income." What I think: 1) There must be a minimum gap between two possible consecutive marks that the examiner can assign. Eg. Suppose that there are N students...
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    Sum of (n+1) terms in exponential series

    Homework Statement S = 1+ x/1! +x2/2! +x3/3! +...+xn/n! To find S in simple terms. Homework Equations None The Attempt at a Solution I tried with Taylor's expansion, coshx and sinhx expansions. But cannot see consequence.
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    A Reasonable length of forecast horizon in a time series

    Suppose we have monthly totals of observed data for last 35 years. That data is of inflow of a river in a reservoir and monthly demands from the reservoir. We are interested to check the effect of construction of a dam in the upstream. The effect is, whether the downstream reservoir will have...
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    Find the minimum of c(3a+4b) when a^2+b^2 +c^2=1.

    Homework Statement Given a,b,c real and a^2+b^2 +c^2=1, to find the minimum of c(3a+4b) Homework Equations The Attempt at a Solution No positive clue yet.
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    Homework inequality -- Show that (a+1)(b+1)(c+1)(d+1) < 8(abcd+1)

    Homework Statement For a,b,c,d >1, Show that (a+1)(b+1)(c+1)(d+1) < 8(abcd+1) Homework Equations How to show this? The Attempt at a Solution I could show for two variables, (a+1)(b+1)<2(ab+1). Tried C-S, AM-GM inequalities in different form and variable transformations. But still no result...
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    B To show of 5[SUP]√2 [SUP] >7, logically.

    Stuck at the simple looking homework problem of my student: To show 5√2 >7, logically.
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    I Counting the number of sets.

    Came to know about the following problem from a friend which can be simplified to the following: A1, A2, ....Am and B1, B2,...Bn are two groups of sets each group spanning the sample space. Now there are p elements in each of Ai and each element is in exactly p1 of the sets of the A group...
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    Total internal reflection: Question on angle of reflection.

    Homework Statement Suppose light from is moving from water to air. The critical angle be θ i.e. for angle of incidence θ, the angle of refraction is 90°. Refractive index of water wrt air be μ. Suppose the angle of incidence (i) is increased by 1° to θ+1. What happens to the...
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    Number of ways to go to the opposite corner.

    # of ways to go to the opposite corner. Suppose m+1 parallel (laid N-S)roads cross n+1 parallel (laid E-W) roads. In how many different ways one can move from North- East corner (of crossing) to South- West corner heading either West or South? What the simplest / attractive way (explanation)...
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    Confusion about defn. of Surjective mapping in WIKI.

    Reference:,_injection_and_surjection Consider the two sets X & Y connected by a the relation y^2=x^2. (For simplicity we can take X={-2,2} and Y={-2,2}).Then can we call the mapping from X to Y to be surjective? From the definition of WIKI, the answer...
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    Standard deviation in Excel.

    By definition standard deviation has divisor 'N' . But in Microsoft Excel the "STDEV" function gives 'N-1' as divisor. This may not be major issue to many of the people. But the command "STDEV" makes many users feel that this is standard deviation, i.e. it has divisor 'N'.
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    Thoughts on an identity.

    Given that 1/ f(cx) = k - g(x) and 2/ the above is an identity, where f(.) and g(.) are two functions and c, k are real valued constants. The problem is to infer upon the types of f(.) and g(.). I have a hunch that f(.) and g(.) are logarithimic functions. Can any one provide...
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    Judgement of good fit: where to stop?

    I have to fit a curve to predict Y on the basis of X. 50 pair of (x,y) is given. On free hand plot the curve it is seen (and otherwise known also) that Y and X has 1:1 relationship. The basic nature of movement of Y is quite composite and found involving x^a, sin(c+bx), d^x , one additive...
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    Any possible lower bound!

    Looking for some positive valued simple functions which are less than (or equal to) the following two integrals (given in the following post).By simple I mean that they may not involve integrals or imaginary components or some infinite series. Again, the functions may not be as simple as f(x)...