7.If X is a continuous RV whose PDF is given by Find c.and mean of X. f(x) = (c(4x-2x²), 0

Q: What values of a and b make the function f continuous everywhere? I -4 if z<2 H-2 az² – bz = 18, if…

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Q: Suppose that a PDF for a continuous variable X is given by if 0 x)=3/4

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Q: 4. Is the function given by G(x) 1 x-1 the interval (0, ∞)? Why or why not? continuous over

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Q: (x. v) = (0, 0)

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Q: 2) Find a value of c for which f (x) is a pdf on the f(x) = cx + x², [0. 1]

A: Introduction ∫-∞∞fxdx=1 The total area under the curve fx of pdf is 1.

Q: If f(3) = 11, f' is continuous, and • f*F(x) f(4) = f'(x) dx = 15, what is the value of f(4)?

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Q: Given f(x) is a continuous function. If f( – 5) = 1 and f'(x) > 4 for – 5 <x < 2, what is the…

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Q: Determine the values of the constants a and b which make the function f(x) below continuous at x =…

A: A function f(x) is continous at x = a when:

Q: 5. Let X have the pdf f(x) = 5x¹, 0 < x < 1, zero elsewhere. Find the pdf of Y = - 2ln(X).

A: The random variable X has the pdf given below: fx=5x4,   0&lt;x&lt;1 The transformed variable is…

Q: If f(x)=5+2(x-1)^1/2, does f(x) satisfy all the conditions of the mean value theorem in the interval…

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Q: Suppose that a continuous function g satisfies: g(x)dr = 30 and g(2x)dx = 3. 0. 2 Find r9(3x²)dx.

A: Suppose that a continuous function g satisfies: ∫03gxdx=30 and ∫06g2xdx=3. The, we have to find the…

Q: If I have a continuous, smooth (no sharp points) function with 3 local maxima and 2 local minima,…

A: Since the function is continuous , with 3 local maxima and 2 local minima.the function will have 5…

Q: Is the function given by g(x) = x²-3x continuous at x = 4? Why or why not?

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Q: Suppose that f is a continuous function such that | f(x) dz = -12. Find (*") dr.

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Q: Let f(x) = 1- 5x2. Use the limit definition of the derivative to show tl f'(x) = –10x

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Q: If F(x)= 27 0<x <3 then pdf f(x): 9. .2 9X II

A: F(X)=x327 , 0&lt;x&lt;3we have to find probability density function.

Q: Q/ if fx(x)= x and (g) is function of R.V X find the PDF of g(x)= X² ?

A: # Given: pdf of random variable x is f(x)=x  then to find pdf of y=x^2 ?

Q: Suppose that f(x) is a function with f(180) = 35 and f'(180) = 10. Estimate f(180.5). f(180.5)

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Q: 7. Determine where the function is continuous. (a) f(x) = 1+x (b) g(x) = sinx+x² + x + 1. x² (c)…

A: This is a problem related to continuity of thr function. Please follow the procedure given below.

Q: 4. Find the derivative of r°(x+ 1)² y = Vr – 3x2 |

A: First i i have written the quotient rule of derivative , just use them for given function and get…