Recent content by rosh300

i think i get it now let: f(x) = 1 \mbox{(the pdf for U[0,1]), }g(y) = e^y = x \Rightarrow \frac{dx}{dy} = e^y, f(g(y)) = 1 this gives you f_x(x) = \int_0^1{1 dx} = \int_{log(0)}^{log(1)}{e^y dy} = \int^0_{-\infty}e^y dy get the pdf fo y from that and use the def/formula for mean and...

Homework Statement find the mean and varince of Log(X) Where X~U[1,0] (X is continuous Random variable) Homework Equations \mathbb{E}(X) = \int_{-\infity}^{\infity}{x f_X(x)} dx \mathbb{E}(X^2) = \int_{-\infity}^{\infity}{x^2 f_X(x)} dx Var(X) = \mathbb{E}(X^2) -...

i think i got it: its f(x,y)_{xy} = \left\{ \begin{array}{rl} \frac{1}{\pi} &\mbox{for } x^2 + y^2 \leq 1\\ 0 &\mbox{otherwise} thanks

Homework Statement \D = \{(x,y) \in \mathbb{R}^2 | x^2 + y^2 \leq 1\} i.e. a disc or radius 1. Write down the pdf f_{xy} for a uniform distribution on the disc. Homework Equations The Attempt at a Solution f_{xy} = \frac{(x^2 + y^2)}{\pi} \mbox{for} x^2 + y^2 \leq 1 0...

Homework Statement \D = \{(x,y) \in \mathbb{R}^2 | x^2 + y^2 \leq 1\} i.e. a disc or radius 1. Write down the pdf f_{xy} for a uniform distribution on the disc. Homework Equations The Attempt at a Solution f_{xy} = \frac{(x^2 + y^2)}{\pi} \mbox{for} x^2 + y^2 0 \mbox{otherwise} as the...

let n be the number of passengers and p be the probability they won't turn up. (a)find prob less than or equal to 5 don't turn up (b)similar thing as (a)

let x, y, z be sides of the box. try to maximise the volume first to find the relations between x, y, z

Homework Statement \Omega is a set of points \omega ; C_{i} i = 1, 2, ... 7 are subsets of \Omega; and ( \Omega, F, P) = (B_{i}, i/10, i = 1, 2, 3, 4 ) is a probability modal with B_{1} = C_{1} \cup C_{7}, B_{2} = C_{2} \cup C_{6}, B_{3} = C_{3} \cup C_{5} and B_{4} = C_{4}. State...

Homework Statement Let a1, a2 are real numbers, where n > 1 show that: determinant of: | 1 a1 a21 ... ... an-11 | | 1 a2 a22 ... ... an-12 | : : | 1 an a2n ... ... an-1n | = \prod (aj - ai) 1\leqi<j<n Homework Equations if you row reduce a matrix...

By basic i mean something which is linear independent and spans V and by factors i mean suppose a1, a2, a3 ... an were the roots, then the factors would be (x - a1), (x - a2), (x - a3) ... (x - an) I suppose i should specfy the Real roots

Homework Statement Find the dimensions and basis of the following vector space V over the given field K: a) V is the set of all polynomials over R (real) of degree at most n and whose coefficients add to 0, K = R (real numbers) b) K = R (real), and V is the set of functions from R to R which...

12^x = 4X8^(2x) take logs of both sides: log(12x) = log(4 X 82x) Get rid of the power 2 (althought not essential) log(12x) = log(4 X 64x) Split RHS using the laws of logs and bring the powers out: x log(12) = log(4) + x log(64) see if u can do the last step (hint collect all terms with x)

Homework Statement Define a paddock to be a set in which A1 - A4, M1 - M4 and D holds but instead of 1\neq 0, we have 1 = 0. Find an example of a paddock, and show that your example is the only oneHomework Equations A1 - A4, M1 - M4 and D are all axioms addition axioms A1: a + b = b + a A2...

thank you for reply just for completeness the second part of the question was to: Find a Bijection [a,b] --> R where a, b are real numbers and b > a this can easily be done by modifying the second example as shown: let g(x) = x /(b-a) (to transform it into the inteval (0,1) ) and f(x) =...

thank u for ur reply and understand how it will work. would : f(x) = 1/(2x-1) work as if x < 1/2 it will be -ve and if x > 1/2 it will be +ve as x --> 1/2 form 0 it will go to -ve infinity as x --> 1/2 form 1 it will go to +ve infinity or f(x) = arctanh(2x - 1) which will transform the...