3. The density function of X is given by f(2) = {"* + bx? 0sxs 1 otherwise If E[X] = ; find a and b.

Q: 43. Log-normal distribution. Let X be N (0, 1), and let Y = eX; Y is said to have the log-normal…

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Q: Find g(e, 1) when g(x, y) = ln ⁡ ( x y + y − 1 )

A: Given function

Q: 16. Let a thin rod of length a have density distribution function p(x) = 10e-0.1, where x is…

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Q: Let h(x) = V4+ 3f(x) with f(1) = 7 and f'(1) = 4. Find the value of h'(1).

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Q: 2. Let X be continous with pdf f(x) = 1/x² if 1 < x < ∞, and 0 otherwise. (a) Does E(X) exist? (b)…

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Q: 2. Aprobability mass function is given as f(x) =- for x = 0,1,2,3,. Find P(1.5 < X < 4.2)

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Q: 1. X is uniform in the range [0,2]. Obtain the pdf of Y=- loge(2-X). What E(Y)?

A: The random variable X follows the Uniform distribution over 0 to 2i.e. X~U(0,2)The PDF of X islet…

Q: 1.5 Solve the below problem: Let Y, and Y, have a joint density function given by fU1, 92) = (3y1 0<…

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Q: With the known values of a = 200,000  and b = 230,000,  the first equation for the probability…

A: Here, a = 200,000 and b= 230,000 f(x) =1/(230000-200000)        =1/30000

Q: Between 3 players (A,B, & C) 5 orange, 5 yellow, and 5 purple balls are divided randomly in a way…

A: In given information it is clear that, there are totally 15 balls (5 orange, 5 yellow and 5 purple )…

Q: Consider a thin wire of mass m and length L going from x = a to x = b. Let the density of the wire…

A: Given that a thin wire of mass m and length L going from x=a to x=b. The density of the wire is…

Q: Consider the density function below: J2(1-x),0<x<1 f(x) = 0, otherwise Computer the following: а.…

A: Solution: 4. From the given information, the probability density function of x is

Q: Suppose X is exponential with parameter λ and Y=e X. Find pdf Y using cdf metho

A: Let X has exponential distribution with parameter λ. The pdf for X is, fx=λe-λx,x&gt;0

Q: Compute ∆y and dy for y = x^2 − 4x when changes from x = 3 to x = 3.5.

A: Topic:- application of derivatives

Q: Let X ~ exp(rate = 3). (a) Find the mgf of X. (b) Use the mgf to find E[X], Var(X), E[X4] and E[X").

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Q: USE SALT Based on the reported sample mean and sample standard deviation, explain why it is not…

A: Given: The paper 'The Effects of Adolescent Volunteer Activities on the Perception of Local Society…

Q: Two college students are studying for an exam. Student X is smarter than sudent Y. The grade that…

A: The joint pdf for X and Y are given as:

Q: (b) For a differentiable function f(x), show that 8(2 = 1) where f' = dj ]dx and a; are the values…

A: We will use the following properties of Dirac delta function to prove the given formula : ∫abδxdx=1…

Q: The weekly demand X for kerosene at a certain supply station has a density function given by [x for…

A: a) P12≤X≤32=P12≤X≤1+P1≤X≤32=∫121xdx+∫13212dx=x22121+12x132=122-1222+1232-12(1)=58

Q: Let f(x) = e*g(x), where g(0) = 1 and g'(0) = 4. Find f'(0). %3D %3D

A: fx=exgx Differentiating with respect to x, we get f'x=dexdx·gx+dgxdx·ex…

Q: Let h(x) = If f(2) = 1 and f'(2) = -1, find h'(2). A B C OD E A. 36 B. 27 C. 12 D. -12 E. 48

A: Step 1:To solve the problem, let's break it down step by step.Given the function:h(x)=[f(x)x​]3We…

Q: Use the information in the following table to find h' (a) at the given value for a. f(x) g(x) f'(x)…

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Q: 8. X is a voltage that is uniform in [-2,2]. X is passed through a device with the output as 0, X 0…

A: The random variable represents the voltage.and X follows the uniform distribution(-2,2) I.e.…

Q: Given that f(z) = z'h(z) h(- 1) = 3 h'(-1) = 6 %3D Calculate f'(- 1).

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Q: 2 a- If the continuous RV X has Rayleight density f(x) = a? x U(x), find E(X") and deduce the values…

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Q: If f(x) and g(x) represent two curves then Area between x=a and x=b is given by a. Ob. ({x) –…

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Q: Let X have the pdf 1 p(x) = T(1+ a2)' x E R. %3D Find the pdf of Y = X?.

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Q: A small market orders copies of a certain magazine for its magazine rack each week. Let X - demand…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: If h (z)=3-2x+5 ln (z+4) then determine h' (1). h' (1) = Number

A: h(x)=3-2x+5lnx+4d dx(xn)=nxn-1d dx(constnat)=0d dx(lnx)=1x

Q: A care antenna is four meters long (starting at x = 0) and has a density of p(x) = Vr+e². %3D

A: Given data:   The expression for the density of the antenna is ρ(x)=x1/2+e-x. The given length of…

Q: Where is the function f(z) = Log(z2 + 1) holomorphic? What is its derivative in the region where it…

A: The function f(z)=log(z2+1) is holomorphic in the region where its argument, z2+1,does not vanish.…