2. Suppose X and Y each have an exponential distribution with parameter a, find the joint p.d.f of X and X + Y. (PS: X and Y are independent r.v. And jointly continuous.) 3. In the situation of (ii) above calculate E[X | X + Y].

Q: 1. Evaluate + 4yz dV E where E = [0,2] × [1,3] × [=1, 1]. %3D

A:

Q: 12. Find r, where log2(ar) – log,(3 – r) = log,(r), and 0 < a < 3. %3D

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Q: (1+z)e- 0(1+0) 0, if a > 0 otherwise,

A: Given,     fx=1+xe-xθθ1+θif x&gt;00otherwisewhere θ&gt;0 If the function follow PDF the…

Q: Prove that E(x) %3D Write the cumulative distribution function F(x).

A: The E(X) can be calculated as ∫0∞x·fxdx And the cumulative function F(x) is defined as Fx=PX≤x

Q: 7. Let g(x) = (x² + 4)°. Find g"(x).

A:

Q: 1. You have the following PDF: f(x) = {1/9 1 ≤ x ≤ 10} (e) Calculate P(2 < X < 5). (f) Calculate P(X…

A: Given;PDF of X is :f(x)=19 ;   1≤x≤10

Q: If f(x) = 2х+1 *,x = 0, 1,2, 3, 4 25 %3D P(2 < X < 4) Select one: O a. 7/25 O b. none О с. 16/25 O…

A:

Q: If g(x) = 3 + x + e*, find g¯'(4).

A:

Q: Q8. Let f(x)= Ln(土) dt (6) Evaleata f'(10) = ? (b) Enlnts (Fツ (o)=? (f-)) (6) =?

A:

Q: di J f(x) dx

A: Given, ddt∫f(x)dx Clearly ∫f(x)dx will be a function of x only. Let ∫f(x)dx=g(x)

Q: 100 30. f(t) =D 62n=1고 %3D

A: We know that exponential series

Q: %3D 1. Given f(x) = k(x – 3), find the value of k if f-1(5) = 2. %3D

A: Given that fx=kx-3To find :value of k if f-15=2Solution:if we find inverse of function then…

Q: 2. Consider the Overlapping Generations model with production studied class. Namely, each generation…

A: The problem pertains to the Overlapping Generations (OLG) model with production. The model features…

Q: Q2 Suppose X and Y are the net profits of two different investments. It is known that they have the…

A: Consider a Random variable R, such that R = wX + (1 - w)Y.   It is given that Sd(X) = 30 and Sd(Y) =…

Q: Find the second order derivation for y = e-3x².

A: d2dx2e-3x2

Q: 2 Calculate e(0) and e(0) for 1.98z E(z) = (z? – 0.9z + 0.9)(z - 0.1)

A: Ez=1.98 zz2-0.9z+0.9z-0.1Now put the value z=0E0=1.9×00-0+0.90-0.1=0Becouse 0x,x≠0⇒0Now E(z)=1.98…

Q: For all x 1 we have

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Q: 7.33. If E[X] = 1 and Var(X) = 5, find (a) E[(2 + X)²]; (b) Var (4 + 3X).

A: E(X)=1,V(X)=5

Q: 65. Let f(u) Find (fog)'(2). Vu and g(x) = u = 1 + 3x. %3D

A: here given  fu=u3, g(x)=u=1+3x2fogx=1+3x23

Q: X and Y are exponentially distributed and independent with densities f(x)=-exp| a a X Obtain P X +Y

A: 8. From the given information, X and Y are exponentially distributed and independent.…

Q: The average rate of change of h(x) over the interval [a, b] is zero and b > a. Part A: What can we…

A: A) The average rate of change = change in outputchange in input…

Q: of the function f(x) =e* the value of e 0.2 2. Use the linearization at a=0 to approximate

A:

Q: 1. The E (]x – µ|²) is equivalent to St(x - 4)? f(x)dx + S"(x – 4)²f(x)dx . True O False

A: Solution

Q: 2. Consider the Markov chain X = (Xn)neN with state space I = {A, B, C, D, E, F, G, H} and one step…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: 8. Let A(x) =| f(t)dt where the graph of f(t) is shown below. Calculate the following. %3D 4. 3. 2.…

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Q: Let w = Ax - By where A and Bare rx q an rx p matrices of known constants and y and x are random…

A:

Q: 1. Show that: 11 (*; - (*)*f; = (x*) – (x)² j=1 a. What is the assumption for f; for the above…

A: Let X be a discrete random variable such that X=x1, x2, …, xn. Then, the variance of the random…

Q: 4. Show that for the exponential distribution dP = yo e The mean and S.D. are both equal to o and…

A: