Theorem 5.4. Let X be a continuous r.v. with p.d.f. fx(x). Let y = g(x) be strictly monotonic (increasing or decreasing) function of x. Assume that g(x) is differentiable (and hence continuous) for all x. Then the p.d.f. h(.) of the r.v. Y is given by : dx hy(y) = fx(x)| (5-22) %3D ... where x is expressed in terms of y, and the range of Y is determined from the given range of the variable X, on using the transformation y = g(x).

Q: Give Three Functions  of Wronskian ?

A: To Give: Wronskian of three functions.   Wronskian:

Q: (4) Use standard multiplication to multiply the two sexigesimal numbers 11, 4; 17, 9 and 50, 50: 43,…

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Q: (4) Prove in two different ways that if a is a positive r number, then (a + 1)" > a" + na"-1:

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Q: Prove that (1, 2) (1,(1), 2, 3).

A: We know, if A and B are two sets then, A is subset of B  if every element in A is also in B.

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Q: verify that (A + B)T = AT + BT

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Q: (f) 1 x + iy + 1 I-iy

A:

Q: (2) Find all the numbers z such that elz = 10i.

A: Consider the given. eiz=10i

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Q: |z+2i|=|z+1- 3i|

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Q: 2. (– 13 + 3i)31

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Q: 1 5. What is equivalent to 81

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Q: Let 1 2 3 1 A = | 6 -2 3 and I3 =| 0 1 5 4 1 If 2. is a real number, compute 2I3 – A.

A: A = 1236-23524 I3=100010001

Q: (a) Show that if a > 0, then 1/a> 0 and 1/(1/a) = a. (b) Show that if a <b, then a < (a+b) < b.

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Q: 3+4i30 -2+i 2-i 5

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A:

Q: (x+1)(x-2)². On what interval (2) (x - 5) let g"(x) = is g Concave up? (Note: you are given g" but…

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Q: |u|> c is true for all real numbers if c _ 0.

A: |u|&gt;c is true for all real numbers if c ____ 0.

Q: MA Let r [-1. 1] and F(x) = f, f(t)dt. where the function f is defined by 1. if x > 0. f(x) = { 0.…

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A: Given: z5=1-i, To find: All values of z.

Q: Use part one of the fundamental theorem of calculus to y = 3x + 7 t 1 + 1³ dt

A:

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A:

Q: If z = 1 - 2j and w= 2 - 3j, express 2. w in the form a + bj where a and b are real.

A: Given  z=1−2jw=2−3j

Q: Let x, y, and z be real numbers. Prove the following a. -(-x) = x b. (-x) * (y) = -(xy) and (-x) *…

A: I have provided detailed proof for each question in the Explanation section.Explanation:Let's go…