36. Assume that X is a continuous random variable with pdf f(x) = exp [-(x + 2)] if -2

Q: Find the equation of the normal line of f(x) = x⁴ + 2x at x = 1 using the limits definition.

A:

Q: For a continuous random variable with the pdf function f(x) = 0.09375(4 - x^2) if 2 0). (b)…

A: a)…

Q: Pr[A'nB]=0.4 and Pr[(AUB)']=0.5. determine Pr[A]

A: GivenP(A'∩B)=0.4P(A∪B)'=0.5

Q: Suppose we have the quadratic function f(x)=A(x^2)+C where the random variables A and C have…

A: A quadratic equation is written as f(x)=Ax2+Bx+C. f(x) has real roots if B2-4AC≥0.

Q: Let X1,..., Xn be iid pdf (log(æ)-®1)² 262 1 f(x) -00 < x < o0, and unknown parameters 01 and 02.…

A: Let X1,X2, X3...be iid with pdf, f(x)=1x2πθ2e-(log(x)-θ1)22 θ2          -∞&lt;x&lt;∞   The…

Q: Let f(t) = 3t – 8t + 5e'. - Then f'(t) =

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Q: Let X be a Poisson random variable with parameter k. (a) Show that the moment generating function…

A: Here X~ Poi(k). Then, P(X=x)=e-kkxx!,x=0,1,2,...0,otherwise a.)The Moment Generating Function of X…

Q: 3) Let X be a continuous random variable with PDF x20 fx(x) ={0 otherwise Find E[X], Var[X] and M…

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Q: Determine p' (x) if p(x) = (5x)" and a = 4. .

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Q: a) Determine the value of k. (b) Determine the cdf. (c) Calculate the probability that time to…

A: Here AS PER POLICY I HAVE CALCULATED 3 PARTS ONLYQ X denote the time to failure (in years) of a…

Q: Let X₁, X₂,..., Xn be a random sample from an exponential distribution with the pdf e-/, for 0 < x…

A: Given that The probability density function of X f(x,β)=1/βe-x/β. 0&lt;x&lt;We have to find the…

Q: Let random variable X be uniform in the interval (0, 1). Define random variable Y = aX + b where a…

A: Given that X ~ U0,1 and Y=aX+b such that a≠0

Q: Let p(x) = x³ - 17x² + 11x + 76. Compute p '(x) and use it to find all values of x for which p '(x)…

A:

Q: Assume that Y has a beta distribution with parameters a and 3, so that the pdf of Y is T(a + B)…

A:

Q: (b)* Show that Y' is closed.

A: Actually we shall show, closure of the set = the set. Then this set will be closed.

Q: Let X1, X2, ..., Xn be a random sample having the common pdf f(xr, 0) = exp[-(x – 0)] for r2 0. (i)…

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Q: Suppose f(x) = 6t²√1+tº dt. 1) Evaluate f (2). 2) Evaluate f'(2). 3) Evaluate f"(2).

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Q: Consider a continuous random variable X with the pdf 0 < x < 1 f(x) = { J x, | c/x³, 1<x <∞ Find (a)…

A: The PDF is a probability that a random variable, say X, will take a value exactly equal to x.

Q: In terms of a positive constant k, random variables X and Y have joint PDF [k+3x² -1/251<1/2, fx,y…

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Q: Let p(x) = cx^2 for the integers 1, 2, and 3 and 0 otherwise. What value must c be in order for p(x)…

A: Solution: From the given information, the probability mass function of X is

Q: For an exponential random variable (X) having θ = 4 and pdf given by: f(x) = (1/θ)e^(−x/θ ) where x…

A: We want to find the mean and variance and P(X&gt;3)= ?

Q: - 3 Let f(x) = 8xVæ + x2. f'(x) =

A: Use the derivative for finding the answer.

Q: Let X1, X2, ..., Xn be a sequence of independent and identically distributed random variables having…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: Let X be a random variable with pdf given by 1 f(x)= π(1+x²)' Find Mx (t). -∞ < x <∞.

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Q: If X is a uniformly distributed random variable between -1 and 1 (pdf of x is constant=1/(2pi)…

A: From the given information, fx=12π, -π≤X≤π Given that Y=sin(X) Consider, the distribution function…

Q: prove that P(X)=P(X|F)P(F) + P(X|F')P(F')

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