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Binomial Distribution

If (1-3p)2, (1+4p)3 and (1+p)6 probabilities of mutually exclusive and exhaustive events, find p

If P(A∩B)=0.16 and P(A∪B)=0.64, find the probability of exactly one of the events A and B occurs.

If K is U([0,5]), find the probability that the equation 4x^2+4xK+K+2=0 has real roots.

Show that p_j is of the form (1-a) a^j and determine a.

What is the probability that the ration of the shorter to the longer segment is less than 14

If p(x) be zero elsewhere except at x=−1,0,1 and p(0) = 14, E[X] = 14 , then find p(-1) and p(1).

Uniform Distribution

If the pdf is f(x)=ax+bx^2 for X in [0,1] and f(x)=0 elsewhere, find the values of a and b.

If the pdf is f(x)=a+bx for X in [1,2] and f(x)=0 elsewhere, find the values of a and b.

If X and Y are Independent with V(X)=V(Y)=V(Z)=1 and √3^k .X+2^k.Y=√5^k.Z, then find the value of k.

If the pdf is f(x)=ax^2+bx for X in [0,1] and f(x)=0 elsewhere, find the values of a and b.

Covariant Differentiation of Covariant and Contravariant Tensors

Christoffel Symbols of the Second Kind

Christoffel Symbols are not Tensors in general

Christoffel Symbols of the First Kind

Derivative of a Tensor is not a Tensor in general

Angle between Tensors

Generalized Inner Product Spaces

Raising and Lowering Indices

If the pdf is f(x)=ax+b for x in [0,2] and f(x)=0 elsewhere, find the values of a and b.

Exercise on Metric Tensor

Metric Tensor

Orthogonality in Inner Product Spaces

Tensor Operations

Invariants

Higher Order Tensors

Covariant & Contravariant Tensors of Order One

Inner Product Space is Uniformly Convex

Inner Product Space is a Normed Space