Determine the value of c for which the function below will be a probability density functi So(8x' - x*) if0sxs8 f (x) =- || otherwise

Q: The probability density function of the time to failure of an electronic component in a copier (in…

A: The time to failure of an electronic component in copier follows Exponential Distribution with pdf…

Q: A random variable is called a power law random variable ifP(X > t) = max{1/(t^α), 1}for some α.…

A: Power law distribution:A random variable, X is said to have a power law probability distribution,…

Q: The amount of electricity consumed (in kWh) on a randomly chosen day in a warenouse Can probability…

A: Given that  Probability density function f(x) f(x)=30/x2     , 25<x<150           0…

Q: The lifetimes X and Y (in years) of two machine components have joint probability density (5 – x –…

A:

Q: Let the random variable X follow a gamma distribution with α = 4 and β = 4. If Y = X2 what is the…

A: Given, X~ Gammaα=4,β=4 Y=X2

Q: A random variable X has the probability density function f(x) = e* on it support [0,z]. What is its…

A:

Q: . When a movie is released in a movie theater, it is this film-ad-this-film-ad that alternates all…

A: From the given information, it is clear that, the movie's play time is regarded as a uniform density…

Q: The probability density function of time, x required to complete an assembly operation is uniformly…

A: Solution: Let X be the time required to complete an assembly operation. From the given information,…

Q: The cumulative distribution function of a random variable X is defined by the equation if x 1…

A: The cumulative distribution function of a random variable X is defined by the equation Fx=0…

Q: Let sinx 0 <x<n f(x) = otherwise be probability density function of X, Compute var(x)?

A: The variance of X is defined as Var(X) = E(X2) - (E(X))2

Q: kA x2 A is a PDF for any value A where A and kare constants and find its Verify f(x) = - associated…

A: Hello! As you have posted 2 different questions, we are answering the first question. In case you…

Q: The probability density function for the time to failure in years of the engine on a car is given by…

A:

Q: The total elaim amount X made in one year on a portfolio of iavuance policies has probability…

A:

Q: If X has an exponential distribution with parameter 0, use the distribution function techniques to…

A:

Q: The random variable X has probability density function 1 < x < 2 f(x) = otherwise. Calculate Var(4X…

A:

Q: - (주), f(x) = 00 < 0, o V27

A:

Q: ) Find the mean and standard deviation of the random variable whose probability density function is…

A:

Q: ). The Exponential probability density function (PDF) is given by: = 2 imulative density function…

A: P(X &gt; s+ t | X &gt; s ) = P(X &gt; s + t , X &gt; s)P(X &gt; s)

Q: The moment generating function of the random variable X having the probability density function f(x)…

A: Given a probability density function of x, we need to find moment generating function of X

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

A: Sample space, S

Q: The density function for a continuous random variable X on the interval 1 ≤ x ≤ 2 is f (x) =…

A: Given:  Density function  fx=105x2

Q: Suppose X is a continuous random variable having probability density function (PDF) f(x). Which of…

A:

Q: At a restaurant, the density function for the time a customer has to wait before being seated is…

A:

Q: The amount of time in hours that a computer functions before breaking down is a continuous random…

A: For continuous random variable, a probability distribution function f(x) is valid if ∫-∞∞f(x) dx=1…

Q: If the probability density function of random variable is given by f( x ) = sinh 2x ; 1<x<2 a. find…

A: a)

Q: 2 3. on the interval 0 < x < 3, use technology (or calculus) to 1 Given the pdf f(2) = -(--)…

A:

Q: (a) A lamp has two bulbs, each of a type with average lifetime 1300 hours. Assuming that we can…

A: Exponential Distribution: A continuous random variable X is said to follow exponential distribution…

Q: The probability density function of the time to failure of an electronic component in a copier (in…

A: Computing the probability that a component lasts more than 1,156 hours before failure:Define the…

Q: The life expectancy of a smartphone's battery X in days is a continuous random variable with…

A:

Q: A factory is supplied with grain at the beginning of each week. The weekly demand X, thousanfd…

A: Given function is f(x)={2(1-x)   for 0≤x≤10            otherwise

Q: The thickness of a wooden shelf in mm, has probability density function             f(x) = {0.75 –…

A: Given :  The thickness of a wooden shelf in mm, has probability density function   f(x) = {0.75 –…

Q: A continuous random variable has a probability density function of f(x) = 2x² for 0 < x≤ 2 and is…

A: Given that  A continuous random variable has a probability density function of f_{x}(x) = 2x2 for 0…

Q: The time it takes for a student to finish an aptitude test (in hours) has a density function of the…

A: Note: Hey, since multiple sub parts are posted, we will answer first three sub parts according to…

Q: A large company has determined that the function f (x) = 3x, 0 <x<1 serves as a payroll density…

A: Answer : The value of G=0.5

Q: If X and Y are two random variable with the joint probability density function give by : f(x, y) = {…

A:

Q: A random variable X has probability density function for 0 < x < 2, 4 f(x) = { +(2x –- 3) for 2 < x…

A: Given:

Q: The probability density function of a continuous random variable is given by 1 1 4 --X f (x): 4 for…

A: The probability distribution is given by: f(x) =(1/4)e(-x/4)    for x&gt;0

Q: probability density function for (X, Y) is as follows. Compute the probability that neither railroad…

A: Here given joint pdf  Using integration finds the required probability

Q: Verify Property 2 of the definition of a probability density function over the given interval. f(x)…

A:

Q: A random variable X has probability density function given by for 1 < x < 3 f(x) = otherwise.…

A: Given probability density function ,fx=14x for 1≤x≤30  otherwise

Q: The continuous random variable X has the probability density function (pdf) given by: 5<x<6…

A: We have been given the pdf as, f(x) = k+5+x       5&lt;x&lt;60                  otherwise Since it…

Q: that a certa heavy equipment can be used before it fails beyond repair is variable having the…

A: We are given a probability density function, say f(x). P(X≥x) = ∫x∞f(x)dx P(a≤x≤b) = ∫abf(x)dx

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: The continuous random variable X has the probability density function (pdf) given by: [k-5+x S(x) =…

A:

Q: Derive the maximum likelihood estimate of the parameter "a" in the probability density function…

A:

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

A:

Q: Choose the best answers. If a random variable X has fınitely many possible values, then X must be […

A: If a random variable x has finitely many possible values ,then must be

Q: A test instrument needs to be calibrated periodically to prevent measurement errors. After some time…

A: The following information has been given: The probability density function (pdf) is given as: f(x)…

Q: f(x) = kx³/² 0 ≤ x ≤ 5 and 0 otherwise.

A: Solution

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!