Using Stokes’ theorem evaluate where
and C is the circle
Solve Numerically --
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A random variable X has the following probability distribution:
Calculate E(X)
a) Obtain the divergence of the following vector field:
show that
b) Determine the metric coefficients for the coordinate system (u,v,z) whose coordinates are related to the Cartesian coordinates by the following equations:
Is the system orthogonal?
a) Determine the value of the constant a for which the vector field
is incompressible.
b) Show that for any vector field \bar
a) Calculate the volume of the tetrahedron whose vertices are the points A = (3, 2, 1), B = (1, 2, 4), C = (4, 0, 3) and D = (1, 1, 7).
b) For three vectors
An unbiased coin is tossed three times. If A is the event that a head appears on each of the first two tosses, B is the event that a tail occurs on the third toss and C is the event that exactly two tails appear in the three tosses, show that:
i) Events A and B are independent
ii) Events B and C are dependent.