Math Answers

Let u = <-6, -2>, v = <-2, 3>. Find -3u + 2v

Given that P(X=2)=9P(X=4)+90P(X=46) for a Poission distribution variate X. Find (i)P(X<2) (ii)P(X>4) (iii)P(X>=1).

Among 100,000 women with negative mammograms, 20 will be diagnosed with breast cancer in 2 years, whereas 1 woman in 10 with positive mammograms will be diagnosed with breast cancer in 2 years. Suppose that 10% of the general population of woman will have a positive mammogram. What is the probability that a woman who develops breast cancer over the next 2 years has a negative mammogram?

A certain disease is spread by only direct contact. The probability of a healthy person to get infect by a single direct contact is 0.02. What is the chance that a healthy person gets infected with the disease by the fourth time he comes into contact with an infected person. (assume contact with the other person is independent)

how to do score limits intervals and find widths

1. The polynomials ax^3+3x^2−13 and 2x^3 - 5x + a are divided by (x+2). If the remainder in each case is the same, find the value of a.

2. What must be subtracted from 4x^4 - 2x^3 - 6x^2 + x - 5 so that the result is exactly divisible by 2x^2 + x - 1? Use long division method.

3. What must be added to x^4 + 2x^3 - 2x^2 + x - 1 so that the result is exactly divisible by
x^2 + 2x - 3 ? Use long division method.

4. If a+b=1, then prove that a^3 + b^3 + 3ab = 1.

5. Factorise:
a) 2√2a^3 + 16√2b^3 + c^3 − 12abc
b) 2√2x^3 + 3√3y^3 + √5(5−5√6xy)

6. Factorise: a / b x^2 + (a / b + c / d)x + c / d; { b not equal to 0, d = 0 }

7. Factorise: (ax - by)^3 + (by - cz)^3 + (cz - ax)^3

The joint probability distribution of two random variables X and Y is given below. Find the marginal distributions and P(Y=3/X=2)
f(x,y) x
y 2 4
1 0.1 0.15
3 0.2 0.3
5 0.1 0.15

Let A,B, C be three events suich that P(A)=0.4, P(C)=0.3, P((A ) ̅ ∩B)=0.2 and P(A∩B)=0.1 and
P(A∩B)=0.1 and (A∪B)∩C=∅
Find a) P(A∪B∪C) b) P(A ̅ ∪ B ̅)

A shipment of 100 digital voice recorders contains 25 that are defective. If 10 of them are randomly chosen for inspection what is the probability that 2 of the 10 will be defectiveby using the Hyper geometric distribution by approximating the hypergeometirc probability by the binomial probability