The length of a wire used in an electrical component is supposed to be 10cm. The machine that stamps out the parts hasn't been recalibrated recently and is making the wires (10 +y) cm long where y varies from wire to wire according to the probability density function 0

Q: Suppose that the probability density function of the length of computer cables is f (x) = 2x/(52)…

A: Let X be the continuous random variable which denotes the length of the computer cables. The…

Q: We are throwing darts at a board with radius 5.  The board has a disk-shaped bullseye with radius 1.…

A:

Q: Suppose X is an exponential random variable with parameter 1/2, and let Y = 14 X^2 + 7. Compu the…

A: Given that X is an Exponential random variable with parameter 1/2. fx=12e-12x, x>0 Given that…

Q: According to the Maxwell-Boltzmann law of theoretical physics, the pdf of V, the velocity of a gas…

A:

Q: Suppose X1,  X2, X3 denote a random sample from the exponential distribution with density function.…

A: A continuous random variable X is said to follow the exponential distribution if its probability…

Q: The time (in hours) required to repair a machine is exponentially distributed 1 with parameter 2 =…

A: Givenλ=13A random variable x~Exponential(λ=13)F(x)=P(X≤x)=1-e-xλ   ; x≥0

Q: If a dealer’s profit, in units of $5000, on a new automobile can be looked upon as a random variable…

A: The E(X) is calculated as follows: E(X)=2∫01x(1-x)dx=2∫01(x-x2)dx=2(x22-x33)01 =2(12-13)=13

Q: The Boris and Bela Pharmacy have determined that the shelf life of B5 Nutrient is a Continuous…

A: Sample space, S

Q: Based on my experience, the number of years, Y, a Cubs fan must wait for a World Series victory is a…

A: Pdf given f(y) = 1/50e^(−y/50) ;y > 0

Q: Suppose that a three-point specialist makes a 3-point basket 37% of the time. IfXis the number of…

A: It is given that the three-point specialist makes a 3-point basket 37% of the time.

Q: can you explain how you get P(X=x)xP(Y=y). is this the joint probability mass function?

A: It is given that,  X~ Poisson(ϕ) and Y~ Poisson (ϕ)

Q: The failure rate of a non-repairable component in a mechatronic system has been determined as h(t) =…

A: The failure rate is given bywant to determine the probability that the component will fail between…

Q: f(y0) = 30 y² exp{-0y³} provided y ≥0 where > 0 is a parameter. (a) Verify that f(y) belongs to an…

A: a) To verify that the probability density function (PDF)  belongs to an exponential family in…

Q: The amount of time required to serve a customer at a bank has an exponential density function with a…

A: Given: Exponential pdf is as fx=ke-kx   0<x<∞ Mean = 3

Q: Find the mgf of the random variable Y = e¬^X when X ~ Exp(X). What is the name of the distribution…

A:

Q: A lamp has two light bulbs with an average lifespan of 1400 hours. Assuming we can model the…

A:

Q: The probability density function for the length of time of postal clerk spends with a customer…

A:

Q: The molecular weight of a particular polymer should fall between 750 and 1,035. Thirty samples of…

A: The answer is attached below,

Q: Suppose PX) = 0.75 and AY2/X) = 0.40. What is the joint probability of X, and Y? (Round your answer…

A: Given that P(X1)= 0.75 and P(Y2|X1)=0.40We have to find P(X1 and Y2)

Q: The bearing capacity of the soil under a foundation is measured to range from 200 kPA to 450 kPA.…

A: Given: The probability density function within the bearing capacity range (200  kPa to 400 kPa) of…

Q: The number of work accidents that occur per week in a mine follows Poisson's law so that the…

A: It is given that P(X = 2) =(3/2) P(X = 1). That is,

Q: 3. The storm runoff X (in cubic meters per second, ems) can be modeled by a random variable with the…

A: a) From the properties of probability density functions, we know : ∫xf(x).dx=1 Therefore,…

Q: Suppose that the probability density function of the length of computer cables is f (x) = 2x/(32)…

A: Let X be the continuous random variable which denotes the length of the computer cables.The…

Q: A lamp has two light bulbs with an average lifespan of 1000 hours. Assuming we can model the…

A: given data x= time when bulb failsμ = 1000 hoursx follows exponential distributionP(x<X) =…

Q: The life X (in hours) of a battery in constant use is a random variable with exponential density.…

A:

Q: A machine has a useful life of 4 to 9 years, and its life (in years) has a probability density…

A: given pdf function fx=115+13xand x= machine has usefull life ; 4 ≤x≤7

Q: The diameter of a particle of contamination (in micrometers) is modeled with the probability density…

A: Given,f(x)=2x3   ;  x>1

Q: A catalyst researcher states that the diameters, in microns, of the pores in a new product she has…

A: Givena)X be diameters, in microns of the pores in a new product are exponentially distributed with λ…

Q: The probability that an event will not happen is PE′=0.79. Find the probability that the event will…

A: The probability that an event will not happen isP(E')=0.79

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.