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For what values of x, 0≤x<2π is it true that cscx=√(cot^2x+1)?
a. 0<x<π b. π<x<2π c. π/2≤x≤3π/2
d. 0≤x<π/2, π<x<3π/2 e. None of these
a. 0<x<π b. π<x<2π c. π/2≤x≤3π/2
d. 0≤x<π/2, π<x<3π/2 e. None of these
There are three urns, urn 1 having 5 white and 3 black balls, urn 2 with 4 white and 4 black balls and urn 3 with 3 white and 5 black balls. A fair die is tossed and
i) urn 1 is chosen if dice shows up 1,2 or 3,
ii) urn 2 is chosen if dice shows up 4 or 5,
iii) urn 3 is chosen if dice shows up 6.
2 balls are drawn at random from the chosen urn. What is tha probability that one of the balls drawn is white and the other black ?
i) urn 1 is chosen if dice shows up 1,2 or 3,
ii) urn 2 is chosen if dice shows up 4 or 5,
iii) urn 3 is chosen if dice shows up 6.
2 balls are drawn at random from the chosen urn. What is tha probability that one of the balls drawn is white and the other black ?
Obtain the maximum likelihood estimate of X in
F(y,X)=(1+X)y^X, 0<y<1
F(y,X)=(1+X)y^X, 0<y<1
If a random variable U has t- distribution with n degrees of freedom, show that Z=U^2 has the f- distribution with 1 and n degrees of freedom.
In a certain community, 10% of all people above 50 years of age have diabetes. A health service in this community correctly diagnoses 95% of all person with diabetes as having the disease, and incorrectly diagnoses 5% of all person without diabetes as having the disease. Find the probability that a person randomly selected from among all people of age above 50 and diagnosed by the health service as having diabetes actually has the disease.
using finite difference, show that the data f(-3)=13, f(-2)=7,f(-1)=3,f(0)=1,f(1)=1,f(2)=3,f(3)=7. represents a second degree polynomial. obtain this polynomial using interpolation and find f(2.5).
a table of values is to be constructed for the function f(x) =1 /1+x in the interval [1,4] with equal step length. determine the spacing h such that quadratic interpolation gives result with accuracy 1×10 - 6
2 kg of water is heated from 0°C to 100°C and converted into steam at the same
temperature. Calculate the increase in entropy, given that specific heat of water is
4.18 × 103
J kg−1
K−1
and Latent heat of vaporisation is 2.27 × 107
J kg−1
.
temperature. Calculate the increase in entropy, given that specific heat of water is
4.18 × 103
J kg−1
K−1
and Latent heat of vaporisation is 2.27 × 107
J kg−1
.
Solve the following ordinary differential equation:
(a) dy/dx=(y-x)/(x-4y)
(b) (2yx^2+4)dy/dx + (2y^2x-3)=0
(c) y"+3y'-10y=3x^2
(a) dy/dx=(y-x)/(x-4y)
(b) (2yx^2+4)dy/dx + (2y^2x-3)=0
(c) y"+3y'-10y=3x^2
use modified euler 's method to find the approximate solution of IVP y' =2xy, y(1)=1, at x=1.5 with h=0.1. if the exact solution is y(x) =ex2-1, find the error.
