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...
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.
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...
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.
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...
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...
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...
# 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)...
Reference: http://en.wikipedia.org/wiki/Bijection,_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...
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'. Misleading...is...
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...
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...
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)...