3. Suppose that the probability density function of X is -{ 0 x>0 %3D 0. elsewhere Determine the cumulative distribution function of X.

Q: 3. The proportion of people who answer a survey sent by mail is a variable continuous random X that…

A: The probability density function of X is given as:

Q: Q. 5 Once a fire is reported to a fire insurance company, the company makes an initial estimate, X,…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: 3. Suppose it is known that the proportion of students who get an A in a particular statistics…

A: Given information: X∼Beta(α=5 and ß=2)f(x)=Γ(α+ß)Γ(α)Γ(ß)xα-1(1-x)ß-1 , 0<x<1   Find:…

Q: 1) Let X₁, X₂, X3....X₁ be a sequence of independent and identically distributed with the following…

A: Given X~N(mean=θ, variance σ 2=1)

Q: 3. Suppose W is a continuous random variable with density function if x 1, fw (x) = |1- |2| if –1<…

A: Let W  is a continuous random variable with a density function                  fW(x)=0           if…

Q: 27. If the probability density function of X is s(z) = { a³ 0, otherwise. then E(X) is 3 A. 4 В. C.…

A: Given,f(x)=3x2a3           0≤x≤a

Q: 5. Let X₁, X2,..., Xn be a random sample from a population with the probability density function x²…

A:

Q: What is the minimum number of units x that will produce a profit, given the following revenue and…

A:

Q: 4. a. The density function of a continuous random variable X is given by f(x)= xe* for x>0. Given…

A:

Q: 7. If the joint probability density function of X and Y is 1 if 0 < x < 1; 0 < y < 1 f(x, y)…

A:

Q: 14. Let (x1, x2, .., an) be independent samples from the population with distribution de- scribed by…

A:

Q: 3. A production facility contains two machines that are used to rework items that are initially…

A:

Q: Find the mathematical expectation and the variance of g(X) = 4X + 3. %3!

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: QUESTION 5 1 is The Final value of F(s) FIE s+3

A: We Use following Theorem to find result.  Final Value Theorem of Laplace Transform  Statement : Let…

Q: 4 9. Let p(x) for x > 0 (and p(x) = 0 if x < 0). T(1+(2x)²) (a) Show that p is a probability density…

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Q: 1. Verify whether the following functions are probability density functions: (1) f(x)=ke-kx (11)…

A:

Q: A system consisting of one original unit plus a spare can function for a random amount of time X. If…

A: From the given information, fx=Cxe-x2, x&gt;0 The value of C is obtained below:…

Q: What is the probability density function of W =min{X, Y }

A: Answer: Let X and Y be two independent random variables with identical probability density function…

Q: 9. Is the function defined by f(x)=0 = 1 18 =0 (2x+3) x4 a probability density function? Find the…

A:

Q: 1) Let X₁, X₂, X3,... X be a sequence of independent and identically distributed with the following…

A: Given that For given pdf we have to proof that it is a one parameter regular exponential family of…

Q: 15. The proportion of people who respond to a certain mail-order solicitation is a continuous random…

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Q: 10. If a continuous random variable has the density function fe) = 0.003x? ,0 <x< 10 then P(X <…

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: A function g(r) is a probability density function if f9(r)dr = 1. Determine if the function if x 0…

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Q: 6. Roughly, speaking, we can use probability density functions to model the likelihood of an event…

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Q: (a) f(x) =-(x² + 4); 0<x <!

A: We know that,   This is not a probability density function

Q: 6. Let the joint probability density function for (X, Y) be f(x.y) - ; e"Y, 1 2 0 < y< ∞, - y< x <…

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Q: Find theprobabilities that it will take on a value (1) between 1 and 3 (2) greater than 0.5.

A:

Q: 2. A random variable has a probability density function given by f(x) = { } ² 0 ≤ x ≤ 2, otherwise.…

A: Given that

Q: 5. Prove or refute the following: If f(x) and f(x) are two probability density functions, then a…

A: Given that, if f1(x) and f2(x) are two probability  density functions.

Q: 4. Two populations with known pdf's, that is, ₁, i = 1,2 has SN (₁, 0², a), where X~ SN (μ, o², a)…

A: There are  populations with known pdf's has  if the density function:The standard normal…

Q: 1. A continuous random variable X is given by a probability density function, x+k , 0sx<2 12…

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer three sub-parts at a…

Q: 3. A function is defined as (0 f(x) = 2x+3 18 0 x 4 Show that f(x) is a probability density…

A:

Q: 6. Given the joint probability density function f(x, y)=10xy, 0<x<y<l, find P(X+Y <1).

A:

Q: 4. The density function of the random variable X is given by 6x(1-x) for 0 1) X

A:

Q: 5. Suppose the probability density function of the magnitude X of a dynamic load on 3 +-x 0<x<2 8 a…

A:

Q: 2. Find the value of k if the following are probability density functions: (1) f(x)=k(1+x) 2≤x≤5 (1)…

A:

Q: 6. The probability density function of (lifetime of an electronic component in years) X is x² P(-112…

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!