0.25 0.00 0.0 1.0 2.0 3.0 4.0 5.0

Q: Determine the enclosed area between f(x) and g(x).

A:

Q: c) Which input yiekds a minimum value of g? d) On which interval(s) is g(x) increasing? e) Compute…

A: (c) To find: The input that yields a minimum value of g. Explanation: It can be seen from the graph…

Q: 1. Find the area between the curve f(x)=√x and g(x) = x³.

A:

Q: Suppose that tP30 = 1 - 3600 500, 0 <t < 60, find the density of T(40).

A: The function pxt is the probability that a life which is aged x will survive t more years. In terms…

Q: Let x. et dt. Find the average value of f on the interval [0, 1].

A:

Q: Approximate the area under the t - curve, with degrees of freedom 29, to the right of t = 2.462…

A: The degrees of freedom is 29.

Q: Find the average rate of change of the absolute value function (a) on [h, 0] if h 0. (c) Express…

A: we know absolute value function isf(x)=xa.average rate of change on[h,0] if h&lt;0let A represent…

Q: Which of the following best describes a dilation of any object about a center point by a scale…

A: The answer is Option 2

Q: Consider the density curve plotted below: Density Curve 0.275 0.25 -0.225 0.2 0.175 0.15 0.125 0.1…

A:

Q: Find the average rate of change of the :following function over the given interval f(1) = r° + 1…

A: Given

Q: Let "X" denote the tensile strength of a variety of metal samples with unit 107 Pa. Solve for the…

A: Solution

Q: a. Determine the average rate of change (AROC) of h with respect to v over the following intervals:…

A:

Q: Find the density of Z

A:

Q: An open-top box is made by cutting equal squares of side x out of the  corners of a piece of…

A:

Q: Find the exact area between the curve f (x) = 9 – x², the x-axis, and x=-3 and x=3.

A:

Q: The velocity of a car was read from its speedometer at 10-second intervals and recorded in the table…

A: Consider the given table for the velocity of a car read from its speedometer at 10 second intervals.…

Q: Use Definition 2 to find an expression for the area under  the curve y= x3  from 0 to 1 as a limit.

A: Make a partition of the intervals [0,1] in n subintervals. ∇xi=1-0n=1nxi=i1n

Q: find the total area between the curve g(x)=x^3 + 2x^2 -x-2 and the x-axis, from x=0 to x=2

A:

Q: Calculate the average rate of change of the given function f over the intervals [a, a + h] where h =…

A: Consider the function f(x) = 38·x2.To find the average rate of change of the function over the…

Q: State the two basic properties of every density curve.

A: Density curve is a type of curve which is mainly drawn to show the probabilities.

Q: y y = flx) 4 8.

A: Given,fx is a decreasing function Left endpoint gives upper estimateRight endpoint gives lower…

Q: @) Find the average densily of the rod. (b) Graph the function neatly orer the interval o to8 and…

A:

Q: Consider the density curve below. 0.4- 0.2+ + 1 2 3 4 56 Find the percent of the area under the…

A: In this case, the entire area is under the density curve. We know we have to find the percentage of…

Q: What would the height need to be for this curve to be a density curve? 8 10 11 12 13 14 15 16 17 18…

A:

Q: Let - fot² Find the average value of f on the interval [0, 1]. f(x) = dt.

A:

Q: Find the area of the region between the curve and the​ x-axis. ​f(x)=36−x2​, from −8 to 8.

A: The function is given by fx = 36-x2;  -8≤x≤8 To evaluate : The area of the region between the curve…

Q: The density function of the time to failure in years of the gizmos (for use on 200 widgets)…

A:

Q: Given the graph of the function f(x) below, use a midpoint approximation with 4 rectangles to…

A: Width of each interval = (6-2)/4= 4/4= 1 So the partition is 2 , 3, 4, 5, 6 So the midpoints are 2.5…

Q: Consider the density curve plotted below: Density Curve 0.11 0.1 0.09 0.08 0.07 0.06 0.05 PDF(X)

A: From the given plot, f(x)=116-6=110, 6&lt;X&lt;16 Consider,…

Q: A new running track is to be constructed in the shape of a rectangle with semicircles at each end.…

A: the total area of the region is covered by a rectangle and 2 semi-circles  we have been given the…

Q: what are the necessary and sufficient conditions for a function to be of continuous density?

A:

Q: ii, Find the area under the graph y=5x4 between the limits x= 1 and x-3.

A:

Q: Find the average valne o the function corect to 2 dp. for fle)= %3D for |<x<4

A:

Q: Let f(x) = -a² + 6æ – 5. Estimate the area below the curve y = f(x) and above the x-axis using 100…

A: Let f(x)=-x2+6x-5 To estimate the area below the curve y = f(x) and above the x-axis using 100…

Q: Show that X N(u, o) belongs to the 2-parameter exponential family of densities.

A:

Q: Given the graph of the function f(x) below, use a midpoint approximation with 3 rectangles to…

A:

Q: Find the area of the region enclosed by the following functions.

A: The given two curves:y=x3-3x+3 and y=3x2-2x.We need to find the area enclosed by the curves.

Q: Find the area between the curves f(x) = x2+2x+1 and g(x) = x+1

A: We need to find area between given curves.

Q: Let f(x) is density function then

A: Continuous distribution: Properties for probability density function: Let f(x) be the probability…

Q: 7. Find the area bounded by the curve y = x e¯** , the x-axis and the maximum ordinate.

A:

Q: Find the area between the curves f(x) and g(x) 2. f(x) = 3x, g(x) = x² – 3x + 8

A: We will find the area between the two curves.

Q: Find the total area under the curve f(x) = 2xer² from a 2xe from x = 0 and a

A:

Q: . Find the area between the curve f(x) = √x and g(x) = x³.

A:

Q: Given the function f(x)=−x−2, find the total area between f(x) and the x-axis over the interval…

A: To find the area of the given region which may lie both above and below the x-axis.

Q: Let f(x) = VT. Find the average value of f on [0, 27].

A:

Q: Find a function that models the area A of an equilateral triangle in terms of the length x of one of…

A: We know the height (h) of an equilateral triangle with the length x of one of its sides is: A =…

Q: Consider the density curve plotted below: Density Curve 20 16 * 12 0.02 0.04 0.06 0.08 0.1 PDF(X)

A: Given: The density function is shown below

Q: Find the area of a triangle bounded by the y axis, the line f(x) = 3 – z, and the line perpendicular…

A:

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!