[1] The probability density function of a random variable X is (c(x+ 4), -44.

Q: 2. Identify the probability density function, then find the mean and variance without integrating.…

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Q: 15 fxy(x,y)= 32 is a joint probability density function over the range 0<x<2 and 0<y<x. Find E(XY).

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Q: 3. Suppose that the probability density function of X is [3x?, lo, 0 < x< 1 f(x) = otherwise…

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Q: For the continuous probability function f(x) = 2kx? e-* when x 2 0. Find a. value of k %3D b. mean

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Q: Let X be a random variable with pdf f(x) = kx*,-1 <x< 1. Find E (X).

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Q: Suppose that the joint probability density function of X and Y is fxy(x,y) = 300.125(x² – y²) e-7*,…

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Q: For the following problems let p(x) = C(2x - x²). a. Find the value C so that p(x) is a probability…

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Q: The joint probability density function of X and Y is given by 6 ху fxy (x, y) = (x² +) 0 <x < 1, 0…

A: Given information: The two random variables X and Y has a joint density function as: fXYx,y=67x2+xy2…

Q: The random variable Y has probability density function fv) = k(y+ y³), 0 < y< 2 and zero otherwise,…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: Consider now a different joint probability density function for X and Y, namely | 12ye-3x-2y² |0 if…

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Q: 4) Suppose X follows Exponential(2), and Y follows Exponential(4). X,Y are independent. (If Z…

A: The answer to the above question is as follows : X~exp(2)f(x)=2e-2x…

Q: For the continuous probability function f(x) = 2kx² e¬* when x > 0 a. value of k %3D b. mean

A: Integration of continuous random variable is 1.

Q: Let f(x) = 0, C:C x² +1¹ 0, if x ≤ 0 if 0<x<√e-1. if x ≥ √e-1 For what value of c is f(x) a…

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Q: 4) Suppose the probability density function of the magnitude X of a dynamic load on a bridge (in…

A: The sum of probabilities of all the outcomes is always equal to 1. Therefore, the area under the…

Q: Consider the probability density function x, for 0 < x < 1 f(x) = {2 - x, for 1 < x <2 0, %3D…

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Q: If the probability density function of X is : f(x) = e-x (1+e*)2 en what is the probability density…

A: It is an important part of statistics. It is widely used.

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

A: Solution

Q: If f(x) = kx, determine the value of k that makes f(x) a probability density function on 0<xs4.

A: Given,           fx=kx2To find : Determine tha value of k that makes fx a probability density…

Q: IF X has an exponential distribution with the parameter 0 an Hy = 202, where 0 >0 then find µx, a,…

A: Given that X has exponential distribution with parameter θ. μx=2σx21θ=2*1θ2θ=2 Therefore,…

Q: A lamp has a lightbulb with an average lifetime of 4 hours. The probability density function for the…

A: Probability density function is

Q: What should be the value of k for f(x) to be able to be a probability density function? f(x)=(2kx)/6…

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Q: Given the probability density function as below (hx² f(x) =} (-15xs 1) otherwise

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Q: (4x³ : - Suppose X has probability density function Jx(x)={ 0<x<1. : otherwise

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Q: et the density function of a random variable Xt fx(x) = Ox®-1, 0sxs1 0<x<1 ompute the sufficient…

A: The pdf of random variable X is given: fX(x) = θ xθ-1,   0≤x≤1

Q: X follows a gamma distribution with PDF f(x)= 4xe-2, where X > 0 (a) Find E(X), E(X²), and E(X³).…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: Find a value of k that will make f a probability density function on the indicated interval.ƒ(x) =…

A: The probability density function on the indicated interval is given by : fx=kx ; 1, 5 As we know…

Q: b) Find the marginal probability density function of Y, fy (y).

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Q: Find (a) the mean of the distribution, (b) the standard deviation of the distribution, and (c) the…

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

A: Solution

Q: Find a value of k that will make f a probability density function on the indicated interval.ƒ(x) =…

A: Definition used-      The function f(x) is a probability density function, if-     i)  f(x)≥0 for…

Q: 2- If the probability density function of X is : f(x) : -00 <x < ∞ (1+e-*)2 1 then what is the…

A: The distribution function of y is given by…

Q: 1. Suppose that for a certain life the probability density function is fx (x) = 1+x ,x >0 Find (i)…

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Q: 4. By the end of 2021, the percentage, X, of the population (expressed in decimals) that will be…

A: Given data : f(x)=kx , 0&lt;x&lt;10 , elsewhere   a) Finding K using the probability density…

Q: 9- The important properties of the probability density function p(x) was: a- p(x) dx = 0.5 b- P(x)…

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Q: 2. Let X be a continuous random variable with density function f(x)= for 0≤x≤2 0, otherwise Find…

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Q: for the following joint probability density function(pdf) of two continuous random variables X and Y…

A: Solution is given below

Q: For a particular kind of battery, the probability density function for x hours to be the life of a…

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Q: If f(x) = e-& ; 0 3) —

A: Given,f(x)=e-x ;0&lt;x&lt;∞

Q: For what value of c is the function {3 [c/x5 if x 2 1 f(x) otherwise a probability density function?

A: Obtain the value of C. The value of C is obtained as follows; Probability Density function:

Q: Example 1 Let X have the probability density function 2x ,0<x<k f(x) = {kz 0 ,e.w. For what value of…

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

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Q: - y) = (x + y) is a joint probability density 15 ction over the range 0 < x < 3 and 0 < y < 2. P(X <…

A: Given that the joint probability density function of x and y is, Compute

Q: f x is a random variable with a probability density function defined by he form x20 , f(x) = 2xe¬x…

A: Solution

Q: B) The probability density function for the random variable X is given by 0<x<3 f(x) ={(25 – x²), 0,…

A: Given function is,  f(x)=x2, 0&lt;x&lt;3(25-x2), 3≤x&lt;60, otherwise

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

A: Given the joint probability density function of X1,X2 as fx1,x2=1-α1-2e-x11-2e-x2ex1-x2 , 0≤x1 ,…

Q: Q3 If the joint probability density function of X and Y is given by 0 < x < ∞, 0 < y< o∞ f(x, y) =…

A: Ans . Here for calculation of E [ X/Y=y ]  ,  we first calculate marginal distribution of  Y  then…

Q: Given the following probability density function: f(x) = 6x(1 – x) 0 < x < 1 Find E(X2).

A: From the given information, fx=6x1-x, 0&lt;x&lt;1

Q: Suppose X has probability density function fx (x) = e² for x >0 and fx (x)= 0 otherwise . P(2< X <…

A: The given probability density function is: fXx=35e-35xx&gt;00Otherwise For P2&lt;X&lt;7:…

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

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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!