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

Q: 1 The life (in years) of a laptop battery has a probability density function defined by P(x) = -z/3…

A: We have given that the life of a laptop battery has a pdf defined by,     P(x) = f(x) = (1/3)*e-x/3,…

Q: Let X have an exponential distribution with parameter > 0. Find p P[k < X < k +1] = p(1 − p)k . such…

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Q: The probability mass function of X = the number of major defects in an electrical appliance of a…

A: From the provided histogram, The probability distribution table is as follow: x 0 1 2 3…

Q: For the joint distribution function f(x,y)=2 for x≥0,y≥0,x+y≤1 and 0 otherwise Find the marginal…

A: The joint probability function is  f(x, y)=2        for x≥0,y≥0,x+y≤1 0       otherwise

Q: Suppose that, for −1 ≤ a ≤ 1, the probability density function of (X₁, X₂) is given by - f(x₁, x₂) =…

A: Solution

Q: X is known to follow the Beta distribution with the parameter 0 = 1000, a = 2, b = 1. wwwww Define…

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Q: Let X be a continuous random variable with PDF x> 0 fx(x) ={0 0. otherwise Find E[X], Var[X] and…

A: Simple integration

Q: Suppose that, for -1 ≤ a ≤ 1, the probability density function of (X₁, X₂) is given by f(x₁, x₂) =…

A: Solution

Q: Let X and Y are independent and both have exponential distribution, Find fz(z) , if Z=X+Y. Where PDF…

A: We know, X~ExpaY~ExpbZ=X+Y Therefore, fXx=a.e-axu(x)fYy=b.e-byu(y)

Q: Let X and Y has joint probability density function f(X, Y) = 81 - , 0 <x< 3, 0 <y< 3. Find E(X).

A: The joint probability density function is, fX,Y=x2y281,0&lt;x&lt;3,0&lt;y&lt;3

Q: if x 2 1, Let {x2 0, if x < 1. Show that f is a probability density function and that the…

A: Topic:- probability density function  Note:- as per our guideline if more than one question uploaded…

Q: 3) Let X be a continuous random variable with PDF x20 fx(x) ={0 otherwise Find E[X], Var[X] and M…

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Q: Let X be a random sample from a population with pdf f(e|x) = ex°-1,0 0 a. Is Sn sufficient for e.…

A: Given that  X be the random variable having the pdf                  Then we have to find that Sn…

Q: a. Is X discrete or continuous random variable? p. If X is discrete, find its pmf. If X is…

A: The cumulative distribution function is defined as F(x) = P(X ≤ x) Note : According to our…

Q: Find the average value of f(x) = ln x on the interval [1,2].

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Q: uppose that X has mean excess loss e(x) = x +1 for > 0. a) Find S(x), f(x), and h(x).

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Q: 3. Find the average value of the function f(x) = x ln(x²) +1 on [e, e²]. Hint: 4(x In(x) – x) =…

A: Average value of function f(x) in the interval [a,b] is given by:

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

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Q: Let X1, X2 .. with parameters a Discuss the construction of 98 percent C.I for B ,X6 be a r.s.of…

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Q: Let X be an exponential random variable with parameter = 7, and let Y be the random variable defined…

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Q: Let the density function of a random variable X be given by fx(x) = 0x®-!, 0Sxs1 Suppose X1, X,.,…

A: Let the density function of xi's be f(x)=θxθ-1; x∈(0,1) x1 ,x2 ,...,xn be the random sample drawn…

Q: Suppose that X ~ Unif[0, 1] and let Y = e^X. (a) Find the cumulative distribution function of Y .(b)…

A: In particular, the cdf and pdf of X is, Since, ex is an increasing function of x and Rx = [0, 1],…

Q: 10. Let X have the exponential distribution with parameter 1. Find the density function of Y = (X –…

A: We have been given that X has exponential distribution with parameter 1. Thus, the pdf of X is given…

Q: The probability density function of X, the lifetime of a certain type of electronic device (measured…

A: Solution

Q: The distribution function for a random variable X is 2x x > 0 x < 0 1- F (x) which of the following…

A: We know that the distribution function of the random variable X is given byF(x)=∫-∞∞f(x)dxwhere f(x)…

Q: If X has a beta distribution with parameters a and B, show that aß V (X) = (a + B)2 (@ + B + 1)

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Q: Find the average value of f(x)= e^-x on the interval [0,2]

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Q: a) The PDF fy (y) b) The mean E[Y]

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Q: Let (3x2, 0< < 1 p(x) = otherwise Show that p(x) is a probability density function. Compute its…

A: Given:p(x)=3x2,0≤x≤10otherwise

Q: The life (in years) of a laptop battery has a probability density function defined by P(x)=12e−x/2…

A:

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: 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: Let X be the service time which follows exponential distribution with parameter 1 = 0.2. Find the…

A: Given that:  X be the service time having λ=0.2

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: Let X denote 0.025 × the ambient air temperature (˚C) and let Y denote the time (min) that it takes…

A: The regression curve for X as a function of Y=y can be given by the conditional expectation EX|Y=y.…

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 follow the beta distribution with pdf S(x) = K z (1 – 2)² on 0<z< 1. Evaluate the value of K.

A: To find the value of K we will use the fact that the integration of f(x) over whole range of x is…

Q: Let X denote 0.025 × the ambient air temperature (˚C) and let Y denote the time (min) that it takes…

A:

Q: Let Y, and Y, have a bivariate normal distribution. The marginal distribution of Y, is normal with…

A: Given Y1 and Y2 are have bivariate normal distribution. Where marginal distribution of Y1 is normal…

Q: Find the pdf of e^x

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Q: If X and Y each follow an exponential distribution with parameter 1 and are inde- pendent, find the…

A: Given: X and Y each follow exponential distribution and are independent we want to find pdf of U=X-Y

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

A: Given, Xt= sin(Bt), t≥0

Q: 3) Let X be a continuous random variable with PDF 1 x20 fx(x) ={0 otherwise Find E[X], Var[X] and…

A: Let X be the continuous random variable with pdf, fX(x)={1θe-xθ; x≥00; otherwise To find E[x],…

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,…

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Q: Find the slope of the normal line to the graph of g(x) = = at the point where x = 0. sin¯¹(x)+e²

A: Slope of the Normal line to the curve f(x) is -1f'(x).

Q: Suppose the life span of a laboratory animal is defined by a Rayleigh density function with a=0 and…

A:

Q: suppose x has an exponential distribution with probability density function f(x) =2e^-2x, x>0. Then…

A: In question, Given X has an exponential distribution with probability density function f(x) =2e^-2x,…

Q: Suppose that Y₁, Y₂,..., Y, is a random sample from a probability density function in the…

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Q: Suppose that a random variable Y has a probability density function given by Sky³e% ,y>0. f(y) = ,0.…

A: Gamma Distribution: A continuous random variable X is said to follow Gamma distribution with…

Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.