The area under the curve of a chi square distribution X´(19) between 0 and Xá is 0.3, then Xá is equal to:

Q: 2. For the Cauchy distribution: 1 C(x; γ) %3D 2 (X – Xo - TY |1 + a. Derive the mean of the…

A: Given the Cauchy distribution , C(x;γ)=1πγ[1+(x-x0γ)2 ] To derive mean of the distribution and the…

Q: A Cl is desired for the true average (i.e. population mean) stray-load loss u in watts for a certain…

A: Given Information: Population standard deviation σ=3.0 Sample size n=100 Sample mean x¯=58.3 (a) To…

Q: 1. Find the average value of f(x) = „ on [0, 1].

A: Topic = Application of integraion

Q: Find the average value of f (x) = 1/x3 from x = 1/3 to x = 1/2.

A:

Q: graph the function and find its average value over the given interval. 1. ƒ(x) = -3x2 - 1 on [0, 1]…

A: The graph of the following functions is given below.

Q: A continuous random variable Z has range equal to the entire real line with pdf fz(2) =e=/2. Find…

A: We have given that a continuous random variable Z has range equal to the entire real line with pdf,…

Q: 3. For t-distribution with 14 degrees of freedom, find the value of ta such that the area between…

A:

Q: In designing an electrical circuit, a probability density function is needed to b integrated to…

A:

Q: In a t-distribution, what is the area under the curve that is to the right of t=2.048 and with…

A: Given,degrees of freedom(df)=28and t=2.048

Q: Find the value of c guaranteed by the Mean Value Theorem of intergrals... Given (x) = on [1,e?]

A:

Q: The slope of the normal line f graph flu)--E at x =1 is:

A:

Q: (a) By a process of repeated sampling from a stationary population, the probability density function…

A: Given:-

Q: Prove that the rv Y=(tan^-1(X1/X2)) and Z=(X1^2+X2^2)^0.5 are independent.   No distribution is…

A:

Q: Find the average value of |x| on the interval [−1, 1].

A:

Q: Graph the function and find its average value over the given interval. g(x) = |x| – 1 on [-1,1]

A: We have to draw the graph and average value.

Q: 6. Find the equation of the normal line to the graph of g(x) = v2-x at x= -7 %3D

A: Definition used -                          The slope of a normal line…

Q: Suppose X1 and X2 are iid observations from the pdf f(x]a) = ax°-le-",x > 0, a > 0. Show that (log…

A: see the attachment.

Q: 21. For the distribution dP = yo e - bxl dx, - 00 Sxs∞ | 1 Hi = 0, o = v2, mean deviation about the…

A:

Q: f (x) = r/ /1+(lnt)² dt

A:

Q: 6. Show that a gamma distribution with a> 1 has a relative maximum at x = (a- 1)B. What happens when…

A: We have to show that : gamma distribution with alpha >1 has a relative maximum at x=(alpha -…

Q: Find the value of t for a t distribution with 19 degrees of freedom such that the area between -t…

A:

Q: The time between successive arrivals of vehicles at a toll booth were observed as follows:" 1.2,…

A: Given:

Q: Find the average value of the function on the given interval. ƒ(x) = x2e2x; [0, 2]

A:

Q: 1. Find the average value of f(x) = on [0, 1].

A:

Q: What is the average value of the function g (x) = 3x on the interval –1 < x < 1?

A: Topic - average value function over interval

Q: Find the average value of ƒ(x) = e2x on [0, ln 2].

A: Given ƒ(x) = e2x . We need to find the average value of a function in the interval [0,ln2].

Q: The area under the curve of a chi square distribution (19) between 0 and X, is 0.05 then X is equal…

A: It is given that, degree of freedom =19 level of significance  =0.05

Q: Find the average value of the function on the given interval. ) = ¹ on [1, 5] X f(x) =

A:

Q: Let X have a gamma distribution with α > 1. Show that E [1/X] = 1/[θ*(α −1)]

A: X~ Gamma(α, θ) Pdf of gamma distribution, f(x)= θαx(α-1)e-θx/Γ(α) ,  0&lt;x&lt;infinite   E(1/X)=…

Q: For a Gamma distribution with rate parameter λ=1 and shape parameter a = 3 ª f(x)=r(a) -xa-1e-ax x>0

A: From the given information, fx=λαΓαxα-1e-λx, x&gt;0 Given that λ=1 and α=3 1. Formula for…

Q: A) | kx 0 1 B) Obtain the 25th percentile and the 75th percentile of the distribution.

A:

Q: Let X have a gamma distribution (a, ß)and Let Y = ex.Find G(y)and g(y) by D F method %3D

A: From the given information, X be a gamma distribution α,β. The pdf for X is, f(x)=βαΓ(α)xα-1e-βx The…

Q: Let X, have a gamma distribution with parameters n/2 and 2 (X, – n)/ /n converges in distribution to…

A:

Q: If X is a uniformly distributed random variable between -1 and 1 (pdf of x is constant=1/(2pi)…

A: From the given information, fx=12π, -π≤X≤π Given that Y=sin(X) Consider, the distribution function…

Q: Let X, have a gamma distribution with parameters n/2 and 2 , and let Y, = log X, .Answer the…

A:

Q: Find the point(s) at which the given function equals its average value on the given interval. 9) y =…

A:

Q: The pdf of a continuous random variable is defined as f(x)= 3k/x3 over [10, ∞) and 0 elsewhere. Find…

A:

Q: Find the area under the t-distribution from t = -2.060 to t = 2.060 when n = 26, then

A:

Q: Let X have a gamma distribution (a, ß)and Let Y = e*. Find G(y)and g(y) by D F method

A: From the given information, X be a gamma distribution (α,β).

Q: find the average value of f(x)=tanx on the interval{0,π/4}

A:

Q: Let X = sin(B1), t20. Give the distribution of X. a)

A: Given, Xt= sin(Bt), t≥0

Q: ) Suppose the diameter at breast height (in.) of trees of a certain type is normally distributed…

A: Given Mean =8.8 Standard deviation=2.8

Q: 1. Use Simpson's rule with four intervals to approximate the value of S e**dx .

A: As per honor code, we will answer first question for you. Please submit the other as a separate…

Q: 8. For the RV X with PDF f(x) = = the mean and the variance of X. 2 X if 0 < x < 1, if 1 < x≤ 2,…

A:

Q: What is the average value of the function f(x) = sin²xcos³x on the interval [0,-]? %D

A: The given function f(x)=sin2xcos3x on the interval 0,π2

Q: Show that for the Gamma distribution e*x dp = 14. dx, 0<x<∞, T() the mean and variance are both…

A:

Q: Find the average value of f (x) = 4 – x² over the interval (0, 3).

A: The average value of the function fx on the interval a,b is defined by Average Value=1b-a∫abfxdx.…

Q: 4 * on the Find the average value of the function f(x) = 3x interval 2 < x < 6

A:

Q: The area under the curve of a chi square distribution '(19) between 0 and x is 0.05 then X. is equal…

A: It is given that, degree of freedom =19 level of significance  =0.05

Q: 1-5* tan (4+) -1 S f (æ) ds at x = 1 Vs2+9 -4

A: Equation of normal at point x=1 is (y-y(1)) = -1/y'(1)(x-1)

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.