45. Consider the exponential random variable X with pdf f(x) = λe-I(0,0) (r). (a) Evaluate the appropriate integral(s) do show that E(X) = \ (b) Evaluate the appropriate integral(s) do show that V(X) = /

Q: n(3x)+sin(5x - 4) - 3 Using Centered Differencing. h = 0.002 O 4.86693212 O 4.876145534 D…

A: Equation is f(x) = ln(3x) + sin(5x - 4) - 3

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A: Given

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A: Follow next step

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A: To estimate the probability distribution from x1 = -2 up to x2 = 1.6 using Romberg Integration, we…

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A: Given, Consider the random variable X which has the pdf, f(x)=k(1-x), 0&lt;x&lt;10,o.w

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A: Given that Y has Gamma distribution with α=3 and β=1.6. Consider,…

Q: Q3) Find the derivative of y for all functions the following (1) y = 0 (sin (In 0) + cos (In 0)),…

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A:

Q: d dx f(x) = ex, f(0) = 8.

A:

Q: Differentiate x *. Hence find [x(2+ x)e* dx.

A:

Q: Let X~n ( x; µ‚10) and p(x > 53 ) = 0.45 Find the value of mean.

A: Given : Let X~n (x; µ, 10) and p(x &gt; 53 ) = 0.45

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…

A:

Q: Suppose that {Xk} k=1,...,n are i.i.d ∼ Exp(λ), the pdf is given by f(x) = λe^(-λx), x > 0. Let Y1…

A:

Q: Let f(x) = 6x4 In(x) + 3 ,5 2. 5 f'(x) = ||

A: The objective is to find the derivative.

Q: etx +1 Differentiate the function f(x) = In e* +1 O e*+1 4ex +1 4e4x ex etx +1 e* +1 4e4x ex etx +1…

A: Please see the explanation below

Q: Find the derivative of the function. Y= q56* In(2)ln(5)ln(6)· 3*. 5".; 2:56*+1+x

A: Given problem:-

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

A:

Q: (a) Calculate the median of X. (b) Note: No need to show the second derivative. Calculate the mode…

A:

Q: If P(A or B) = 0.801, P(B') = 0.33 and P(A and B) = 0.20. Find i) P(B) ii) P(A)

A: Answer: Given that, P(A or B) = 0.801 P(B') = 0.33 P(A and B) = 0.20

Q: Q1 (a) Let X1,..., Xn be iid obser vations from an exponential(A) pdf, where A has the conjugate…

A: Im bayesian probability theory if the posterior distribution p(θ|x) are in the same family as the…

Q: Find all functions f(x) such that 7x f'(x) - and f (0)

A:

Q: A table of values for f, g, f', and g' is given. f(x) g(x) f '(x) g'(x) 1 3 2. 4 1 8 7 3 7 7 9 (a)…

A: Solve the function

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A: The Beta function, denoted as B(x, y), and the Gamma function, represented as Γ(z), are special…

Q: Let F(2) = 2, F'(2) = 3, H(2) = 4, H'(2) = 3. A. If G(z) = F(z)*H(z), then G'(2) = _______ B. If…

A: The Product Rule:The Quotient Rule:

Q: Let {Xi} be i.i.d with the pdf f(x; θ) =c/x^(θ+1)  x > 1, where θ > 0 is the unknown parameter.…

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

A:

Q: Let f(z) = 4z +1 f(2) =

A: Given  f(x)= 4x+1

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A: By the property , the total probability density function is equal to one.

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A: The equation of normal line is 4x+3y-19=0

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A:

Q: 2 [*x* (Inx)² dx

A: Given integration is evaluated.

Q: Let 7(t) = Find 7'(t) デ'() = Answer preview:

A: We have to solve

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A: Step 1: Step 2: Step 3: Step 4: