If a random variable X has a uniform density with theparameters α and β, find its distribution function.

Q: If x is a normally distributed random variable with μ = 18 and o = 2.5, then where will the density…

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

Q: If the probability density of a random variable is given by 0<x<1 f(x) ={2-x 1<x< 2 0 elsewhere…

A: Given,f(x)=x0&lt;x&lt;12-x1≤x&lt;20elsewhere

Q: If the independent random variables X and Y have the marginal densities f(x) = ⎧ ⎪⎪⎨ ⎪⎪⎩ 1 2 for 0…

A: From the given information, it is clear that,  fx=12     0&lt;x&lt;20       elsewhereπx=13…

Q: Let X be a Gaussian random variable with zero mean and variance equal to 2. 1-Find the probability…

A: It is given that, X be a Gaussian random variable with zero mean and variance equal to 2. That is,…

Q: Find the joint probability density of the two randomvariables X and Y whose joint distribution…

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Q: If X has the uniform density with the parameters α = 0and β = 1, use the distribution function…

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Q: 15. An insurance policy reimburses the excess of a loss over 2. The policy- holder's loss, Y,…

A: Y is denoted as the policy holder's loss. It is known, fy=2y3,if y&gt;1            0, otherwise…

Q: A particular fast-food outlet is interested in the joint behavior of the random variable Y1, the…

A: NOTE: Since we only answer up to 3 subparts , we will answer the first 3. Please resubmit the…

Q: 2. If a random variable X has a uniform density with the parameters a=4 and B = 5, find its Density…

A: A random variable X has a uniform density with the parameters α=4 and β=5

Q: (a) Give the marginal density functions for both random variables. Are the independent? (b) What is…

A: f(x,y)=ye-y(1+x)        x,y&gt;0

Q: Suppose that the random variable W has a beta distribution with probability density function f (w)…

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Q: Suppose that the random variable W has a beta distribution with probability density function f(w)…

A: Use the condition of valid pdf to find the value of k…

Q: Find the mean and variance for the distribution of random variable X whose density function is f(x).…

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Q: Let X and Y be two random variables with joint density function

A: Given information: Let X and Y are two random variables with joint probability density function as…

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

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Q: Since P{X=1}=P{X=2}=P{X=3}=0.2 , P{X=4}=0.4 , plot the probability density function of the random…

A: To plot p.d.f. of x, we represent X on X axis and value of probability at X on Y axis.

Q: If the random variable has the density function 2х, 0<x<1, f,(x) = { 0, Otherwise. and the…

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Q: Suppose that the random variable W has a beta distribution with probability density function f(w)…

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Q: If X is a continuous random variable find the CDF and density of the function y = x/3

A: It is given that X is a continuous random variable. Define the random variable y as:

Q: Show that if a random variable has a uniform density with parameters α and β, the probability that…

A: The objective is to show that if the random variable has a uniform density with parameters α and β,…

Q: Show that the mean value and variance of random variable having the uniform density 1 function,…

A: The probability density function of a uniform distribution is given below:

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: If X has a uniform density with α = 0 and β = 1, show that the random variable Y = −2. In X has a…

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Q: 1) Suppose, the continuous random variable X has density given by fx(x) 4.x*; 0 < x < 1, 0;…

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Q: Suppose x is a random variable uniformly distributed over the range, -a <x< a, and y=x?. Find the…

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Q: Suppose X and Y are independent and identically distributed (i.i.d.) random variables, each with the…

A: Given  Two independent and identically distributed random variables are x and y.Both x and y with…

Q: The joint density function of the random varıables X and Y is 6-x- y 0<x< 1, 0 < y<1-x, f(x,y) = 8.…

A: From the given information, fx,y=6-x-y8, 0&lt;x&lt;1, 0&lt;y&lt;1-x

Q: Let the continuous random variable X denote the current measured in a thin copper wire in…

A: Answer - Let the continuous random variable X.  Assume that the range of X is [4.9, 5.1] mA,…

Q: The distribution function of a RVX is given by F(x) = 1- (1+ x)e, x20. Find the density function,…

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Q: Consider the random variable X with the uniformdensity having α = 1 and β = 3.(a) Use the result of…

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Q: x+y) for 2≤x≤6 and 0≤y≤5, 0 otherwise P(3 1), P(X < 3),

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

Q: The joint density function for two random variables X and Y is given by {** +y) if0 < x < 15,0 < y<…

A: From the given information, Consider, the Joint density function of X and Y are given below:…

Q: Find the exact probability density of the sum W = X + Y.

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Q: Show that the characteristic function of random variable having a binomial density is Ox(») =[1– p+…

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Q: show how to generate random variables from a uniform density on an interval (a,b)

A: In the given problem we have to answer the question of, how to generate random variables from a…

Q: If the joint density of X and Y is given byf(x, y) =⎧⎨⎩e−(x+y) for x &gt; 0, y &gt; 00 elsewhere and…

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Q: Let X be a random variable with density x², 1<x<2 f(x)=• 0, otherwise Find F(x), the distribution…

A: To find the distribution function we have to integrate f(x).When x&lt;1 then…

Q: Find the joint probability density of the two randomvariables X and Y whose joint distribution…

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Q: Find the probability density of the sum W = X+ Y.

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Q: 3. If a dealer's profit, in units of $5000, on a new automobile is a random variable X having the…

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Q: If X ~ U(3, 15), what is the probability density function for this distribution?

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Q: Find the mean value of random variable X, if X has the following density function, f(x) = 1-x²,…

A: The mean value of X can be obtained as E(X) = ∫x.f(x) dx

Q: (a) Find the joint distribution of Y1 and Y2: ƒ (y1, y2) (b) Then compute the marginal density of Y1

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Q: Let X be a uniformly distributed random variable with probability density function: fx(x) = {6 Find…

A: First we want to find the value a then after find the distribution of X^2

Q: Let X and Y be two independent poisson random variables with probability mass functions Px (a) =…

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Q: The expected values of the independent random variables x and y (E(x) and E(y)) for a joint density…

A: Given: E(x)=5 E(y)=6   x and y are independent random variable

Q: If the probability density of a random variable is given by |С ехр(-x/4), 0<x<1 fx (x) otherwise…

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Q: Suppose that X and Y are random variables with the following joint density function ,0 <x < 20, 0 <…

A: From the given information, f(x,y)=1, 0≤x≤20, 0≤y≤48, 20y≤48x And U=Y-X

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!