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

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

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Q: Chapter 4, Section 4.3, Question 024 Given the functionf (x) = x³ + 3x² – 45x + 8 over the interval…

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Q: Find f such that f'(x) = 4x² + 3x-3 and f(0) = 9.

A: (1) f′(x)=4x2+3x−3f(x)=∫f′(x)dxf(x)=∫(4x2+3x−3)dxUsing the Power Rule∫xndx=xn+1n+1+C

Q: et X₁, X₂,..., Xn 0 x =df ƒ (x; 0) = ² 0, represent a random sample from a population X with , x>1…

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Q: Use incremental search with Δx = 0.2 to bracket the smallest positive zero in f(x) = x3 - 10x2 + 5.

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Q: Let X1, ..., Xn be iid pdf 1 f(x) = (log(x)–01)² 202 :e -00 < x < ∞, %3D and unknown parameters 01…

A: The given density function is: fx=1x2πθ2e-log x-θ122θ2   -∞&lt;x&lt;∞

Q: ƒ(x) = 6x - 4x 2 x² +1 on [-3,0]

A: Let's find average value of given  function on interval [ -3 , 0 ].

Q: (b). Use the definition of the derivative to evaluate f (x)=x". [Hint: Use the Binomial Theorem:…

A: Given: i. fx=xnii. a+bn=an+nan-1b+nn-12!an-2b2+·····+nabn-1+bn. To Find: Use definition of…

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: If X be a continuous random variable with be -bx if x >0 f(x)= otherwise then the moment generating…

A: The random variables can be categorized into 2, continuous random variable and discrete random…

Q: Let f(x) = ax + b/x. What are the critical points of f(x)? i

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Q: In(x) x² 1 5,00 dx

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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: Let f(x) = ln(x² + 2x + 6) f'(x) =

A: We have to find the derivative.

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: et f'(x) = with the initial condition f(1) = 5. Determine the particular f(x).

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Q: s defined by + x). The value o ind off to 1 decimal

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Q: Let 7(t) = Find 7'(t) 7 (t) =

A: Topic - vectors and derivatives Since r→t = 5 t5-1, -e-t, -3 sin2t we to find r→'t  derivative of tn…

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)…

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Q: Let f(x) = In[x4(x +9)6(x2 + 4)3]. Find f'(x). f'(x) =

A: Given,

Q: B₂ (x₂3x₂ ) = 4x₁x₂ *1*2 0< x₂ <1 2 Y₁ = x₂₁² Y₂ = X₁ X/₂ Find the joint pdf for Y₁, Y₂ for 0<x< ₁…

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Q: Use the Mean Value Theorem to prove that f'(x) = 0.01 has a solution in the (-4, -3) interval.…

A: We use cubic formula to calculate the value of c

Q: 1. Let the random variable Y have pdf as f(y\A) = e®=e=t(e-1), y>0,1>0. Show that W = e – 1] ~ x²…

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Q: f"(x) = 20x3 + 12x2 + 4 with the initial conditions f(0) particular f(x). = 8 and f(1) = 5. Det

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Q: Find the maximum likelihood estimator for θ in the pdf f(y; θ) = 2y/(1 − θ^2), θ ≤ y ≤ 1.

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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: let p(x)=g(f(x)). use the given table to find p'4

A: p(x)=g[f(x)] diff. w. r. to x p'(x)=g'[f(x)] . f'(x)  ..................(1)

Q: 1 -dx x(x² + 1)

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Q: p(x) = x / 5 x = 1,0,1

A: Given, p(x) = x / 5 ;        x = 1,0,1

Q: - 3 Let f(x) = 8xVæ + x2. f'(x) =

A: Use the derivative for finding the answer.

Q: The function f(x)=(1/(x+1))+4 is decreasing on what interval(s)?

A: Consider the function  fx=1x+1+4

Q: Let f(x) = In(x² – 14x + 52) f'(x) =

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

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Q: (b) Verify mean value theorem for f(x)=x² - 5x+6 over the interval [1,3].

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Q: Let 7(t) = Find 7'(t) F'(t) =

A: The objective is to find the derivative of given

Q: Let f(x) = 6x* /T + f'(x) =

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Q: Let h(x) = x³e" k6*. Find dr (h(x)) wherek is a real number (i.e. k is a constant).

A: Given: h(x)=x3ex3-k6x To find: ddxh(x)