The expected or mean value of a continuous rv X with pdf f (x) is Mx = E(X) X·f(x) dx %D Is this statement true or false?

Q: What is / 3d x? S 3dx = 3x + C / 3dx = 3x / 3d x = – 3x+ C S 3dx = – 3x² + C

A: here we need to find the anti derivative of given function. the solution is following.

Q: The graph of f is shown below. Let g(z) = | f(t) dt. Order g(6), g'(6), and g"(6) from smallest to…

A: Introduction: Differentiation under the integral sign is a calculus procedure for evaluating…

Q: et f and g denote differentiable functions. If f'(x) = g (x), then f(x) = g(x).

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Q: - Use the definition of derivative to find the tangent and normal equations of f(x) = (x - 3)2 %3D…

A: We can find the tangent equation and normal equation as below.

Q: Find the derivative

A: The first derivative of f(x) is represented byf'(x) and the second derivative is represented by…

Q: f(x) = [In (x² + 2x + 1)]ª

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Q: If the sign of the first derivative function is positive, the main function f(x) is decreasing.

A: We have to tell If the sign of the first derivative function is positive , the main function f(x) is…

Q: Use the first derivative test to find and classify the relative extrema of x2 +8x+ 16 f(1) = For…

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Q: Given Derivative Sx) = 3x2 + 7x + 1

A: Given function: fx=3x2+7x+1 Basic concept: Here we shall use basic power rule. fx=cxnf'x=cnxn-1

Q: A continuous function has a derivative at every point in a given interval. True or False?

A: function is differentiable means that function is continuous as well as smooth at every point of…

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: 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 has a derivative at x = 2, then f is continuous at x = = 2. True False

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Q: A local grocery store observes that on average 7.25 customers enter the store every five minutes…

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Q: What is the derivative of f(x) sec(tanx)?

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Q: let the pdf f(x) is even function then E(x) is?

A: We know, F(x) is even, Than, F(x) =F(-x) From definition, For even function ( if minimum = - n, than…

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!